NOT 
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A 

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ffimM 


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UNOCCUPIED  LINE. 


V 


TABLES 


LOGARITHMS   OF  NUMBERS 


AND    OF 


SUES  AID  TANGENTS 


FOR   EVERT 


TEN  SECONDS  OF  THE  QUADRANT, 


WITH  OTHER  USEFUL  TABLES. 


BY   EL  I  AS   LOOM  IS,  LL.D., 

FBOFESSOE    OF   NATCBAL     PHILOSOPHY    A?!D   A6TEONOMY   IN    YALE    COLLEGE,   AND    AUTH03    OF   A 
"  COCEljE   OF   MATHEMATICS." 


T  II  I  11  T  V-S  I  X  T  H    EDITION 


NEW-YORK: 

HARPER   &    BROTHERS,    PUBLISHERS, 

329    &    331    PEARL    STREET, 

FRANKLIN   SQUARE. 

1879. 


Ei'-tored  acccrdir.g  to  Act  of  Congress,  in  the  year  one  thousand  eight  hundred  and  fcrty-ei^ht,  by 

Harper  &  Brothers, 
m  tne  Clerk's  Office  of  the  District  Court  of  the  Southern  District  of  New  York. 


CONTENTS. 


P«go 

EXPLANATION  OF    THE    TABLES V 

TADLE    OF    LOGARITHMS   OF    NUMBERS 1 

LOGARITHMIC    SINES    AND    TANGENTS „  21 

NATURAL    SINES    AND    TANGENTS .      .              ...  116 

NATURAL    SECANTS 1 34 

LENGTHS    OF    CIRCULAR    ARCS 135 

TRAVERSE    TADLE .  130 

MERIDIONAL    TARTS 142 

CORRECTIONS    TO    MIDDLE    LATITUDE 149 

LOGARITHM?    FOR    COMPOUND     INTEREST,    ETC .      .  .  ,  .  150 


P  E  E  B  A  C  E. 


The  accompanying  tables  were  designed  to  afford  the  means  of  per- 
forming trigonometrical  computations  with  facility  and  precision.  The 
tables  chiefly  used  in  this  country  for  purposes  of  education  extend  to 
six  decimal  places,  like  those  in  the  present  collection ;  but  the  pre- 
cision which  they  are  designed  to  furnish  is  only  attained  by  a  serious 
expenditure  of  labor.  In  the  Table  of  Logarithms  of  Numbers  they  do 
not  furnish  the  correction  for  a  fifth  figure  in  the  natural  number,  and 
the  labor  of  computing  this  correction  is  such  that  I  always  prefer  the 
use  of  Hutton's  Tables,  extending  to  seven  places,  even  in  computations 
to  which  six-place  logarithms  are  abundantly  competent.  In  the  pres- 
ent collection,  the  correction  for  a  fifth  figure  of  the  natural  number  is 
introduced  at  the  bottom  of  each  page,  and  the  table  is  thus  rendered 
nearly  as  useful  as  one  of  the  common  kind  extending  to  100,000.  The 
whole  has  been  carefully  compared  with  standard  authors,  and  nearly 
a  dozen  errors  have  thus  been  detected  in  the  common  tables. 

The  principal  table  in  this  collection  is  that  of  Logarithmic  Sines  and 
Tangents.  The  common  tables  in  this  country  extend  only  to  minutes, 
with  differences  to  100".  If,  in  a  trigonometrical  computation,  angles 
are  only  required  to  the  nearest  minute,  tables  to  five  places  are  quite 
sufficient ;  but  if  the  computation  is  to  be  carried  to  seconds,  these  can 
only  be  obtained  from  the  common  tables  by  a  great  expenditure  of 
time  and  labor.  In  the  present  collection,  the  sines  and  tangents  are  fur- 
nished to  every  ten  seconds  of  the  quadrant,  and  at  the  bottom  of  each 
page  is  given  the  correction  for  any  number  of  seconds  less  than  ten,  so 
that  the  precision  of  seconds  can  be  obtained  with  almost  the  same  fa- 
cility as  that  of  minutes  with  the  tables  in  common  use.  Moreover, 
near  the  limits  of  the  quadrant,  by  means  of  an  auxiliary  table,  sines  and 
tangents  are  readily  obtained,  even  for  a  fraction  of  a  second.  The 
method  of  arrangement  of  the  sines  and  tangents  was  suggested  by  a 
table  in  Mackay's  Longitude  ;  but  the  errors  of  that  table,  amounting  to 
several  thousand,  have  been  corrected  by  a  careful  comparison  with  the 
work  of  Ursinus.  By  comparison  with  the  same  standard,  more  than 
two  hundred  errors  (chiefly  in  the  final  figures)  have  been  detected  in 
the  tables  in  common  use. 

The  Table  of  Natural  Sines  and  Tangents  is  of  less  use  than  thelo^a- 
rithmic  ;  nevertheless,  it  is  often  important  for  reference,  particularly  in 
analytical  geometry  and  the  calculus  ;  and  it  is  useful  as  a  stepping- 
stone  to  assist  the  beginner  in  comprehending  the  nature  of  logarithmic 


'v  ■££■**■'  "  -'•Preface. 

sines  and  tangents.  The  Traverse  Table  commonly  used  in  this  country 
furnishes  the  latitude  and  departure  to  every  quarter  degree  of  the  quad- 
rant, for  distances  from  1  to  100,  and  occupies  ninety  pages.  The  accom- 
panying table  occupies  but  six  pages,  and  yields  ten  times  greater  pre- 
cision. 

The  Table  of  Meridional  Parts  extends  to  tenths  of  a  mile,  and  great 
care  has  been  taken  to  insure  its  accuracy.  For  this  purpose,  I  have 
compared  all  the  similar  tables  within  my  reach,  and  among  them  have 
found  two  which  appeared  to  have  been  computed  independently.  Be- 
tween them  there  were  detected  674  discrepancies  in  the  final  figures. 
These  cases  were  all  recomputed,  and  78  errors  were  detected  in  the 
best  copy  compared.  It  is  probable  that  the  numbers  in  this  table  are 
not  in  every  instance  true  to  the  nearest  tenth  of  a  mile  ;  but  it  is  be- 
lieved that  the  remaining  errors  are  few  in  number,  as  well  as  minute. 
This  table  is  confidently  pronounced  more  accurate  than  any  similar 
one  with  which  I  have  been  able  to  compare  it. 

The  Table  of  Corrections  to  Middle  Latitude  was  computed  entirely 
anew.  The  corresponding  table  in  common  use,  which  was  originally' 
computed  by  Workman,  contains  more  than  four  hundred  errors,  sev- 
eral of  them  amounting  to  two  minutes. 

On  the  whole,  it  is  believed  that  the  accompanying  tables  will  be 
fcund  more  convenient  to  the  computer  than  any  tables  of  six  decimal 
places  hitherto  published  in  this  country ;  and  that  they  will  be  pro- 
nounced sufficiently  extensive  for  all  purposes  of  academic  and  cohegi- 
ate  instruction,  as  well  as  for  practical  mechanics  and  surveyors. 


EXPLANATION  OF  THE  TABLES, 


Table  of  Logarithms  of  Numbers,  pp.  1-20. 

Logarithms  are  numbers  contrived  to  diminish  the  labor  of  Multiplica- 
tion and  Division  by  substituting  in  their  stead  Addition  and  Subtrac- 
tion. All  numbers  are  regarded  as  powers  of  some  one  number,  which 
is  called  the  base  of  the  system  ;  and  the  exponent  of  that  power  of  the 
base  which  is  equal  to  a  given  number,  is  called  the  logarithm  of  that 
number. 

The  base  of  the  common  system  of  logarithms  (called,  from  their  in- 
ventor, Briggs'  logarithms)  is  the  number  10.  Hence  all  numbers  are 
to  be  regarded  as  powers  of  10.     Thus,  since 

10°=  1,  0  is  the  logarithm  of  1  in  Briggs'  system  ; 

lO^lO,  1     "  "  10  "  " 

10a=l00,        2     "  "  100 

10s=1000,      3     "  "  1000  "  « 

104=  10,000,  4     "  "  10,000  " 

&c,  &c,  &c. ; 

whence  it  appears  that,  in  Briggs'  system,  the  logarithm  of  every  num- 
ber between  1  and  10  is  some  number  between  0  and  1,  i.  e.,  is  a  prop- 
er fraction.  The  logarithm  of  every  number  between  10  and  100  is 
some  number  between  1  and  2,  z.  e.,  is  1  plus,  a  fraction.  The  loga- 
rithm of  every  number  between  100  and  1000  is  some  number  between 
2  and '3,  i.  e.,  is  2  plus  a  fraction,  and  so  on. 

The  preceding  principles  may  be  extended  to  fractions  by  means  of 
negative  exponents.     Thus,  since 


10-1-0.1, 

— 1 

is 

the 

logarithm 

of  0.1 

in 

Briggs'  system 

1(T2=0.01, 

—2 

M 

a 

0.01 

<■(             u 

10"3=0.001, 

—3 

a 

it 

0.001 

a                    a 

10"4= 0.0001, 

—4 

a 

a 

0.0001 

u                     ii 

&c, 

&C, 

&C. 

Hence  it  appears  that  the  logarithm  of  every  number  between  1  and 
0.1  is  some  number  between  0  and  — 1,  or  may  be  represented  by  — 1 
plus  a  fraction;  the  logarithm  of  every  number  between  0.1  and  .01  is 
some  number  between  — 1  and  — 2,  or  may  be  represented  by  -  2  plus 


vi  Explanation   op   the   Tables. 

a  traction  ;  the  logarithm  of  every  number  between  .01  and  .001  is  some 
number  between  — 2  and  — 3,  or  is  equal  to  — 3  plus  a  fraction  and  so  on. 
The  logarithms  of  most  numbers,  therefore,  consist  of  arn  integer  and 
a  fraction.  The  integral  part  is  called  the  characteristic,  and  may  be 
known  from  the  following 

Rule. 

The  characteristic  of  the  logarithm  of  a  number  greater  than  unity,  vs 
one  less  than  the  number  of  integral  figures  in  the  given  number. 

Thus  the  logarithm  of  297  is  2  plus  a  fraction  ;  that  is,  the  character- 
istic of  the  logarithm  of  297  is  2,  which  is  one  less  than  the  number  oi 
integral  figures.  The  characteristic  of  the  logarithm  of  5G73.29  is  3 ; 
that  of  73254.1  is  4,  &c. 

The  charactej-istic  of  the  logarithm  of  a  decimal  fraction  is  a  negative 
number,  and  is  equal  to  the  number  of  places  by  which  its  first  significant 
figure  is  removed  from  the  place  of  units. 

Thus  the  logarithm  of  .0040  is  — 3  plus  a  fraction;  that  is,  the  char- 
acteristic of  the  logarithm  is  — 3,  the  first  significant  figure  4  being 
removed  three  places  from  units. 

The  accompanying  table  contains  the  logarithms  of  all  numbers  from 
1  to  10,000  carried  to  G  decimal  places. 

To  find  the  Logarithm  of  any  Number  between  1  and  100. 

Look  on  the  first  page  of  the  table,  along  the  column  of  numbers  undei 
N,  for  the  given  number,  and  against  it,  in  the  next  column,  will  be  found 
the  logarithm,  with  its  characteristic.     Thus, 

opposite  13  is  1.113943,  which  is  the  logarithm  of  13; 
05  is  1.812913,  "  "  05. 

To  find  (hi  Logarithm  of  any  Number  consisting  of  three  Figures. 

Look  on  one  of  the  pages  from  2  to  20,  along  the  left-hand  column 
marked  N,  for  the  given  number,  and  against  it,  in  the  column  headed  0, 
will  be  found  the  decimal  part  of  its  logarithm.     To  this  the  character- 
stic  must  be  prefixed,  according  to  the  rule  already  given.     Thus 
the  logarithm  of  347  will  be  found,  from  page  8,  to  be  2.540329  ; 
"     871         "  "  "     18,    "     2.940018. 

As  the  first  two  figures  of  the  decimal  are  the  same  for  several  suc- 
cessive numbers  in  the  table,  they  are  not  repeated  for  each  logarithm 
separately,  but  are  left  to  be  supplied.  Thus  the  decimal  part  of  th<; 
logarithm  of  339  is  .530200.  The  first  two  figures  of  the  decimal  remain 
the  same  up  to  347 ;  they  are  therefore  omitted  in  the  table,  and  are  to 
be  supplied. 

To  find  the  Logarithm  of  any  Number  consisting  of  four  Figures. 
Find  the  three  left-hand  figures  in  the  co'umn  marked  N  as  before, 


Explanation  op  the  Tables.  vii 

and  the  fourth  figure  at  the  head  of  one  of  the  other  columns.     Opposite 
to  the  first  three  figures,  and  in  the  column  under  the  fourth  figure,  will 
he  found  four  figures  of  the  logarithm,  to  which  two  figures  from  the 
column  headed  0  are  to  be  prefixed,  as  in  the  former  case.     The  char- 
acteristic, must  be  supplied  by  the  usual  rule.     Thus 
the  logarithm  of  345G  is  3.538574  ; 
"     8765  is  3.942752. 
In  several  of  the  columns  headed  1,  2,  3,  &c,  small  dots  are  found  in 
the  place  of  figures.     This  is  to  show  that  the  two  figures  which  are  to 
be  prefixed  from  the  first  column  have  changed,  and  they  are  to  be 
taken  from  the  horizontal  line  directly  below.     The  place  of  the  dots  is 
to  be  supplied  with  ciphers.     Thus 

the  logarithm  of  2045  is  3.310693  : 
"     9777  is  3.990206. 
The  two  leading  figures  from  the  column  0  must  also  be  taken  from 
the  horizontal  line  below,  if  any  dots  have  been  passed  over  on  the  same 
horizontal  line.     Thus 

the  logarithm  of  1628  is  3.211654. 

To  find  the  Logarithm  of  any  Number  containing  more  than  four 

Figures. 

By  inspecting  the  table,  we  shall  find  that  within  certain  limits  the  log- 
arithms are  nearly  proportional  to  their  corresponding  numbers.     Thus 
the  logarithm  of  7250  is  3.860338  ; 
"  "     7251  is  3.860398  ; 

"     7252  is  3.860458  ; 
"  "     7253  is  3.860518. 

Here  the  difference  between  the  successive  logarithms,  called  the 
tabular  difference,  is  constantly  60,  corresponding  to  a  difference  of  unity 
in  the  natural  numbers.  If,  then,  we  suppose  the  logarithms  to  be  pro- 
portional to  their  corresponding  numbers  (as  they  are  nearly),  a  differ- 
ence of  0.1  in  the  numbers  should  correspond  to  a  difference  of  6  in  the 
logarithms  ;  a  difference  of  0.2  in  the  numbers  should  correspond  to  a 
difference  of  12  in  the  logarithms,  &c.     Hence 

the  logarithm  of  7250.1  must  be  3.860344  ; 
"     7250.2         "       3.860350; 
"     7250.3         "       3.860356; 
&c,  &c. 

In  order  to  facilitate  the  computation,  the  tabular  difference  is  insert- 
sd  on  page  16  in  the  column  headed  D,  and  the  proportional  part  for  the 
fifth  figure  of  the  natural  number  is  given  at  the  bottom  of  the  page. 
Thus,  when  the  tabular  difference  is  60,  the  corrections  for  .1,  .2,  .3, 
&c,  are  seen  to  be  6,  12,  18,  &e. 

If  the  given  numbei  was  72501,  the  characteristic  of  its  logarithm 
would  be  4,  but  the  decimal  part  would  be  the  same-  as  for  7250.1.. 


Vll  1 


Explanation    of   the    Tables. 


If  it  were  required  to  find  the  correction  for  a  sixth  figure  in  the  nat- 
ural number,  it  is  readily  obtained  from  the  Proportional  Parts  in  the 
table.  Thus,  if  the  correction  for  .5  is  30,  the  correction  for  .05  is  ob- 
viously 3. 

As  the  differences  change  rapidly  in  the  first  part  of  the  table,  it 
was  found  inconvenient  to  gi^e  the  proportional  parts  for  each  tabuloi 
difference ;  accordingly,  for  the  first  seven  pages  they  are  only  given 
for  the  even  differences,  but  the  proportional  parts  for  the  odd  differences 
will  be  readily  found  by  inspection. 
Required  the  logarithm  of  452789. 

The  logarithm  of  452700  is  5.655810 
The  tabular  difference  is  96. 

Accordingly,  the  correction  for  the  fifth  figure,  8,  is  77,  and  for  the 
sixth  figure,  9,  is  8.6,  or  9  nearly.  Adding  these  corrections  to  the  num- 
ber before  found,  we  obtain  5.655896. 

The  preceding  logarithms  do  not  pretend  to  be  perfectly  exact,  but 
only  the  nearest  numbers  having  but  six  decimal  places.     Accordingly, 
when  the  fraction  which  is  omitted  exceeds  half  a  unit  in  the  sixth  deci- 
mal place,  the  last  figure  must  be  increased  by  unity. 
Required  the  logarithm  of  8765432. 

The  logarithm  of  8765000  is  6.942752 

Correction  for  the  fifth  figure  4,  20 

"  "       sixth  figure  3,  1.5 

"  "       seventh  figure  2,  0.1 

Therefore  the  logarithm  of  8765432  is  6.942774. 

Required  the  logarithm  of  234567. 

The  logarithm  of  234500  is  5.370143 

Correction  for  the  fifth  figure  6,  111 

"       sixth  figure  7,  13 

Therefore  the  logarithm  of  234567  is  5.370267. 

To  find  the  Logarithm  of  a  Decimal  Fraction. 

The  decimal  part  of  the  logarithm  of  any  number  is  the  same  as  that 
of  the  number  multiplied  or  divided  by  10,  100,  1000,  &c.  Hence,  for 
a  decimal  fraction,  we  find  the  logarithm  as  if  the  figures  were  integers, 
and  prefix  the  characteristic  according  to  the  usual  rule. 

Examples. 

The  logarithm  of  345.6  is  2.538574 

"  "        87.65  is  1.942752 

«  "  2.345  is  0.370143 

«  M  .1234  is  1.091315 

"  «  .005678  is  3.754195. 


Explanation   of    the       ableh  ix 

The  minus  sign  is  placed  over  the  characteristic  to  show  that  this 
alone  is  negative,  while  the  decimal  part  of  the  logarithm  is  positive. 

To  find  the  Logarithm  of  a  Vulgar  Fraction. 
We  may  reduce  the  vulgar  fraction  to  a  decimal,  and  find  its  loga- 
rithm by  the  preceding  rule  ;  or,  since  the  value  of  a  fraction  is  equal  to 
the  quotient  of  the  numerator  divided  by  the  denominator,  we  may  sub- 
tract the  logarithm  of  the  denominator  from  that  of  the  numerator;  the 
difference  will  be  the  logarithm  of  the  quotient. 
Required  the  logarithm  of  T3g,  or  0.1875. 

From  the  logarithm  of  3,         0.477121, 
Subtract  the  logarithm  of  16,  1.204120. 
Leaves  logarithm  of  T\,  or  .1875,  1.273001. 

Tn  the  same  manner  we  find 

the  logarithm  of  /?  is  2.861697 ; 
"    jff  is  1.147401. 

To  find  the  natural  Number  corresponding  to  any  Logarithm. 

Look  in  the  table  in  the  column  headed  0  for  the  first  two  figures  of 
the  logarithm,  neglecting  the  characteristic ;  the  other  four  figures  are 
to  be  looked  for  in  the  "same  column,  or  in  one  of  the  nine  following  col- 
umns ;  and  if  they  are  exactly  found,  the  first  three  figures  of  the  corre- 
sponding number  will  be  found  opposite  to  them  in  the  column  headed 
N,  and  the  fourth  figure  will  be  found  at  the  top  of  the  page.  This  num- 
ber must  be  made  to  correspond  with  the  characteristic  of  the  giver, 
logarithm  by  pointing  off  decimals  or  annexing  ciphers.     Thus 

the  natural  number  belonging  to  the  logarithm  4.370143  is  23450  ; 
"  "  "  "  1.538574  is  34.56. 

If  the  decimal  part  of  the  logarithm  can  not  be  exactly  found  in  the 
table,  look  for  the  nearest  less  logarithm,  and  take  out  the  four  figures 
of  the  corresponding  natural  number  as  before ;  the  additional  figures 
maybe  obtained  by  means  of  the  Proportional  Parts  at  the  bottom  of 
the  page. 

Required  the  number  belonging  to  the  logaiithm  4.368399. 

On  page  6,  we  find  the  next  less  logarithm  .368287. 

The  four  corresponding  figures  of  the  natural  number  are  2335. 
Their  logarithm  is  less  than  the  one  proposed  by  112.  The  tabular 
difference  is  186;  and,  by  referring  to  the  bottom  of  page  6,  we  find 
that,  with  a  difference  of  186,  the  figure  corresponding  to  the  Piopor- 
tional  Part  112  is  6.  Hence  the  five  figures  of  the  natural  number  are 
23356  ;  and,  since  the  characteristic  of  the  proposed  logarithm  is  4,  these 
five  figures  are  all  integral. 

Required  the  number  belonging  to  logarithm  5.345678. 

The  next  less  logarithm  in  the  table  is  .345570 

Their  difference  is  108. 


x  Explanation   of   in  e    Tables. 

The  first  four  figures  of  the  natural  numter'are  2210. 
With  the  tabular  difference  196,  the  fifth  figure  corresponding  to  108 
s  seen  tc  be  5,  with  a  remainder  of  10,  which  furnishes  a  sixth  figure  5 
nearly.     Hence  the  required  number  is  221655. 
In  the  same  manner  we  find 

the  number  corresponding  to  logarithm  3.538672  is  3456.78 ; 
«  "  "  1.994605  is  98.7654; 

"  "  "  T.647817  is  .444444. 

Table  of  Natural  Sines  and  Tangents,  pp.  116—133. 

This  is  a  table  of  natural  sines  and  tangents  for  every  degree  and 
minute  of  the  quadrant,  carried  to  six  places  of  figures.  Since  the  ra- 
dius of  the  circle  is  supposed  to  be  unity,  the  sine  of  every  arc  below 
90°  is  less  than  unity.  These  sines  are  expressed  in  decimal  parts  of  the 
radius ;  and,  although  the  decimal  point  is  not  written  in  the  table,  it 
must  always  be  prefixed.  The  degrees  are  arranged  in  order  at  the  top 
of  the  page,  and  the  minutes  in  the  left  hand  vertical  column.  Directly 
under  the  given  number  of  degrees  at  the  top  of  the  page,  and  opposite 
to  the  minutes  on  the  left,  will  be  found  the  sine  required.  The  two 
leading  figures  are  repeated  at  intervals  often  minutes.  Thus 
the  sine  of  6°  27' is  .112336 ; 
"    28°  53'  is  .483028. 

The  same  number  in  the  table  is  both  the  sine  of  an  arc  and  the  co- 
sine of  its  complement.     The  degrees  for  the  cosines  must  be  sought  at 
the  bottom  of  the  page,  and  the  minutes  on  the  right.     Thus 
the  cosine  of  62°  25'  is  .463038  ; 
"  8 4°  23'  is  .097872. 

If  a  sine  is  required  for  an  arc  consisting  of  degrees,  minutes,  and  sec- 
onds, it  may  be  found  by  means  of  the  line  at  the  bottom  of  each  page, 
which  gives  the  proportional  part  corresponding  to  one  second  of  arc. 

Required  the  sine  of  8°  9'  10". 

The  sine  of  8°  9'  is  .141765. 

By  ieferring  to  the  bottom  of  page  116.  in  the  column  under  8°,  we 
find  the  correction  for  1"  is  4.80  ;  hence  the  correction  for  10"  must  be 
48,  which,  added  to  the  number  above  found,  gives  for  the  sine  of  8° 
9'  10",  .141813. 

In  the  same  manner  we  find 

the  cosine  of  56°  34'  28"  is  .550853. 

It  will  be  observed,  that  since  the  cosines  decrease  while  the  arcs  in- 
crease, the  correction  for  the  28"  is  to  be  subtracted  from  the  cosine 
of  56°  34'. 

The  arrangement  of  the  table  of  natural  tangents  is  similar  to  that  of 
the  table  of  sines.  The  tangents  for  arcs  less  than  45°  are  all  less  thac 
radius,  and  consist  wholly  of  decimals.  For  arcs  above  45°,  the  tan- 
gents are  all  gi  eater  than  radius  and  contain  both  integral  and  decima 


Explanation    of   the    Tables.  xi 

figures.     The  proportional  parts  at  the  bottom  of  each  page  enable  us 
readily  to  find  the  correction  for  seconds.     Thus 

the  natural  tangent  of  32°  29'  18"  is  .636784  ; 
"  "      743  35'  55"  is  3.63014. 

To  find  the  Number  of  Degrees,  Minutes,  and  Seconds  belonging  to  a 
given  Sine  or  Tangent. 

If  the  given  sine  or  tangent  is  found  exactly  in  the  table,  the  corre- 
sponding degrees  will  be  found  at  the  top  of  the  page,  and  the  minutes 
on  the  left  hand.  But  when  the  given  number  is  not  found  exactly  in 
the  table,  look  for  the  sine  or  tangent  which  is  next  less  than  the  pro- 
posed one,  and  take  out  the  corresponding  degrees  and  minutes.  Find, 
also,  the  difference  between  this  tabular  number  and  the  number  pro- 
posed, and  divide  it  by  the  proportional  part  for  1"  found  at  the  bottom 
of  the  page  ;  the  quotient  will  be  the  required  number  of  seconds. 

Required  the  arc  whose  sine  is  .750000. 

The  next  less  sine  in  the  table  is  .749919,  the  arc  corresponding  to 
which  is  48°  35'.  The  difference  between  this  sine  and  that  proposed 
is  81,  which,  divided  by  3.21,  gives  25.  Hence  the  required  arc  is  48c 
35'  25". 

In  the  same  manner  we  find 

the  arc  whose  tangent  is  2.000000,  to  be  63°  26'  6".  f 

Table  of  Natural  Secants,  pp.  134-5. 

This  is  a  table  of  natural  secants  for  every  ten  minutes  of  the  quad- 
rant carried  to  seven  places  of  figures.  The  degrees  are  arranged  in 
order  in  the  first  vertical  column  on  the  left,  and  the  minutes  at  the  top 
of  the  page.     Thus 

the  secant  of  21°  20'  is  1.073561  ; 
"    81°  50'  is  7.039622. 
If  a  secant  is  required  for  a  number  of  minutes  not  given  in  the  table, 
the  correction  for  the  odd  minutes  may  be  found  by  means  of  the  last 
vertical  column  on  the  right,  which  shows  the  proportional  part  for  one 
minute. 

Let  it  be  required  to  find  the  secant  of  30°  33'. 

The  secant  of  30°  30'  is  1.160592. 
The  correction  for  1'  is  198.9,  which,  multiplied  by  3,  gives  597. 
Adding  this  to  the  number  before  found,  we  obtain  1.161189. 

For  a  cosecant,  the  degrees  must  be  sought  in  the  right-hand  vert/eal 
column,  and  the  minutes  at  the  bottom  of  the  page.     Thus 
the  cosecant  of  47°  40'  is  1.352742. 
■» 

Table  of  Logarithmic  Sines  and  Tangents,  pp.  21-115. 

This  is  a  table  of  the  logarithms  of  the  sines  and  tangents  for  every 
ten  seconds  of  the  quadrant,  carried  to  six  places  of  decimals      The  de« 


xii  Explanation    of   the   Tables. 

grees  and  seconds  are  placed  at  the  top  of  the  page,  and  the  minutes  in 
the  left  vertical  column.  After  the  first  two  degrees,  the  three  leading 
figures  in  the  table  of  sines  are  only  given  in  the  column  headed  0",  and 
are  to  be  prefixed  to  the  numbers  in  the  other  columns,  as  in  the  table 
of  logarithms  of  numbers.  Also,  where  the  leading  figures  change,  this 
change  is  indicated  by  dots,  as  in  the  former  table.  The  correction  fcr 
any  number  of  seconds  less  than  10  is  given  at  the  bottom  of  the  page. 

To  find  the  Logarithmic  Sine  or  Tangent  of  a  given  Arc. 

Look  for  the  degrees  at  the  top  of  the  page,  the  minutes  on  the  left 
hand,  and  the  next  less  tenth  second  at  the  top  ;  then,  under  the  seconds, 
and  opposite  to  the  minutes,  will  be  found  four  figures,  to  which  the 
three  leading  figures  are  to  be  prefixed  from  the  column  headed  0" ;  to 
this  add  the  proportional  part  for  the  odd  seconds  from  the  bottom  of 
the  page. 

Required  the  logarithmic  sine  of  24°  27'  34". 

The  logarithmic  sine  of  24°  27'  30"  is  9.617033. 
Proportional  part  for  4"  is  18. 

Logarithmic  sine  of  24°  27'  34"  is  9.617051. 
This  is  the  logarithm  of  .414049  found  in  the  table  of  natural  sines  on 
page  120.  The  natural  sine  being  less  than  unity,  the  characteristic 
of  its  logarithm  is  negative.  Tc  obviate  this  inconvenience,  the  char- 
acteristics in  the  table  nave  all  been  increased  by  10 ;  or  the  logarith- 
mic sines  may  be  regarded  as  the  logarithms  of  natural  sines  computed 
for  a  radius  of  10,000,000,000.    ■ 

Required  the  logarithmic  tangent  of  73°  35'  43". 

The  logarithmic  tangent  of  73°  35'  40"  is  10.531031. 
Proportional  part  for  3"  is  23. 

Logarithmic  tangent  of  73°  35'  43"  10.531054. 

When  a  cosine  is  required,  the  degrees  and  seconds  must  be  sought 
at  the  bottom  of  the  page,  and  the  minutes  on  the  right,  and  the  correc- 
tion for  the  odd  seconds  must  be  subtracted  from  the  number  in  the  table. 
Required  the  logarithmic  cosine  of  59°  33'  47". 

The  logarithmic  cosine  of  59°  33'  40"  is  9.704682. 
Proportional  part  for  7"  is  25. 

Logarithmic  cosine  of  59°  33'  47"  is  9.704657. 
So,  also,  the  logarithmic  cotangent  of  37°  27'  14"  is  found  to  be  10.115744 
The  proportional  parts  given  at  the  bottom  of  each  page  correspond 
to  the  degrees  at  the  top  ol  the  page  increased  by  30',  and  are  not 
strictly  applicable  to  any  other  number  of  minutes ;  nevertheless,  the 
differences  of  the  sines  change  so  slowly,  except  near  the  commence- 
ment of  the  quadrant,  that  the  error  resulting  from  using  these  numbers 
for  every  part  of  the  page  will  seldom  exceed  a  unit  in  the  sixth  deci- 
mal place.     For  the  firs'  two  degrees,  the  differences  change  so  rapidly 


EXFIANATION     OF     THE     TABLES.  xiii 

hat  the  proportional  part  for  1"  is  given  for  each  minute  in  the  right- 
hand  column  of  the  page.  The  correction  for  any  number  of  seconds 
less  than  ten  will  be  found  by  multiplying  the  proportional  part  for  1" 
by  the  given  number  of  seconds. 

Required  the  logarithmic  sine  of  1°  17'  33". 

The  logarithmic  sine  of  1°  17'  30"  is  8.352991. 
The  correction  for  3"  is  found  by  multiplying  93.4  by  3,  which  gives 
280.     Adding  this  to  the  above  tabular  number,  we  obtain 
the  sine  of  1°  17'  33",  8.353271. 

A  similar  method  may  be  employed  for  several  of  the  first  degrees 
of  the  quadrant,  if  the  proportional  parts  at  the  bottom  of  the  page  are 
not  thought  sufficiently  precise.  This  correction  may,  however,  be  ob- 
tained pretty  nearly  by  inspection  from  comparing  the  proportional 
parts  for  two  successive  degrees.  Thus,  on  page  26,  the  correction  for 
1",  corresponding  to  the  sine  of  2°  30',  is  48  ;  the  correction  for  1",  cor- 
responding to  the  sine  of  3°  30',  is  34.  Hence  the  correction  for  1", 
corresponding  to  the  sine  of  3°  0',  must  be  about  41  ;  and  in  the  same 
manner  we  may  proceed  for  any  other  part  of  the  table. 

Near  the  close  of  the  quadrant,  the  tangents  vary  so  rapidly,  that  the 
same  arrangement  of  the  table  is  adopted  as  for  the  commencement  of 
the  quadrant.  For  the  last  as  well  as  the  first  two  degrees  of  the  quad- 
rant, the  proportional  part  to  1"  is  given  for  each  minute  separately. 
These  proportional  parts  are  computed  for  the  minutes  placed  opposite 
to  them,  increased  by  30' ,  and  are  not  strictly  applicable  to  any  other 
number  of  seconds  ;  nevertheless,  the  differences  for  the  most  part 
change  so  slowly,  that  the  error  resulting  from  using  these  numbers  foi 
every  part  of  the  same  horizontal  line  is  quite  small.  When  great  ac- 
curacy is  required,  the  table  on  page  114  may  be  employed  for  arcs 
near  the  limits  of  the  quadrant.  This  table  furnishes  the  differences  be- 
tween the  logarithmic  sines  and  the  logarithms  of  the  arcs  expressed  in 
seconds.     Thus 

the  logarithmic  sine  of  0°  5'  is  7.1G269G  ; 
the  logarithm  of  300"  (=5')  is  2.477121  ; 

the  difference  is  4.G85575. 

This  is  the  number  found  on  page  114,  under  the  heading  log.  sine 
A — log.  A",  opposite  5  min. ;  and  in  a  similar  manner  the  other  numbers 
in  the  same  column  are  obtained.  These  numbers  vary  quite  slowly 
for  two  degrees  ;  and  hence,  to  find  the  logarithmic  sine  of  an  arc  less 
than  two  degrees,  we  have  but  to  add  the  logarithm  of  the  arc  expressed 
m  seconds  to  the  appropriate  number  found  in  this  table. 
Required  the  logarithmic  sine  of  0°  7'  22'-. 

'  Tabular  number  from  page  1  ]  4,  4.685575. 

The  logarithm  of  442"  is  2.64542? 


Logarithmic,  sine  of  0°  7'  22"  is  7.330997. 


xiv  Explanation   of   the    Tables. 

The  logarithmic  tangent  of  an  arc  less  than  two  degrees  is  found  in 
a  similar  manner. 

Required  the  logarithmic  tangent  of  0°  27'  30". 

Tabular  number  from  page  114,       4.685584. 

The  logarithm  of  1656"  is  3.219060. 


Logarithmic  tangent  of  0°  27'  36"  is  7.904644. 
The  column  headed  log.  cot.  A-\-log.  A"  is  found  by  adding  the  log- 
arithmic cotangent  to  the  logarithm,  of  the  arc  expressed  in  seconds. 
Hence,  to  find  the  logarithmic  cotangent  of  an  arc  less  than  two  degrees, 
we  must  subtract  from  the  tabular  number  the  logarithm  of  the  arc  in 
seconds. 

Required  the  logarithmic  cotangent  of  0°  27'  36". 

Tabular  number  from  page  114,  15.314416. 

The  logarithm  of  1656"  is  3.219060. 

Logarithmic  cotangent  of  0°  27'  36"  is  12.095356. 
The  same  method  will,  of  course,  furnish  cosines  and  cotangents  ot 
arcs  near  90°. 

The  secants  and  cosecants  are  omitted  in  this  table,  since  they  are 
easily  derived  from  the  cosines  and  sines. 

The  logarithmic  secant  is  found  by  subtracting  the  logarithmic  cosine 
from  20  ;  and  the  logarithmic  cosecant  is  found  by  subtracting  the  loga- 
rithmic sine  from  20. 

Thus  we  have  found  the  logarithmic  sine  of  24°  27'  34"  to  be  i>. 617051. 
Hence  the  logarithmic  cosecant  of  24°  27'  34"  is  10.382949. 

The  logarithmic  cosine  of  54°  12'  40"  is  9.767008. 

Hence  the  logarithmic  secant  of  54°  12'  40"  is  10.232992. 

To  find  the  Arc  corresponding  to  a  given  Logarithmic  Sine  or  Tangent. 

If  the  given  number  is  found  exactly  in  the  table  the  corresponding 
degrees  and  seconds  will  be  found  at  the  top  of  the  page,  and  the  min- 
utes on  the  left.  But  when  the  given  number  is  not  found  exactly  in 
the  table,  look  for  the  sine  or  tangent  which  is  next  less  than  the  pro-, 
posed  one,  and  take  out  the  corresponding  degrees,  minutes,  and  sec 
onds.  Find,  also,  the  difference  between  this  tabular  number  and  the 
number  proposed,  and,  corresponding  to  this  difference,  at  the  bottom  of 
the  page  will  be  found  a  certain  number  of  seconds,  which  is  to  be  added 
to  the  arc  before  found. 

Required  the  arc  corresponding  to  the  logarithmic  sine  9.750000. 

The  next  less  sine  in  the  table  is  9.749987. 

The  arc  corresponding  Jo  which  is  34°  13'  0". 

The  difference  between  its  sine  and  the  one  proposed  is  13,  corre- 
sponding to  which,  at  the  bottom  of  the  page,  we  find  4"  nearly.  Hence 
the  required  arc  is  34°  13'  4". 


Explanation  of  the  Tables.  xv 

In  the  same  manner  we  find  the  arc  corresponding  to  logarithmic  tan- 
gent 10.250000,  to  be  00°  38'  57". 

When  the  arc  falls  within  the  first  two  degrees  of  the  quadrant,,  the 
odd  seconds  may  be  found  by  dividing  the  difference  between  the  tab- 
ular number  and  the  one  proposed,  by  the  proportional  part  for  1".  We 
mus  find  the  arc  corresponding  to  logarithmic  sine  8.400000,  to  be  1° 
26'  22''  nearly. 

We  may  employ  the  same  method  for  the  last  two  degrees  of  the 
quadrant  when  a  tangent  is  given ;  but  near  the  limits  of  the  quadrant 
it  is  better  to  employ  the  auxiliary  table  on  page  114.  If  we  subtract 
the  corresponding  tabular  number  on  page  114  from  the  given  logarith- 
mic sine,  the  remainder  will  be  the  logarithm  of  the  arc  expressed  in 
seconds. 

Required  the  arc  corresponding  to  logarithmic  sine  7.000000. 

We  see,  from  page  22,  that  the  arc  must  be  nearly  3'  ;  the  correspond- 
ing tabular  number  on  page  114  is  4.685575. 

The  difference  is  2.314425; 
which  is  the  logarithm  of  206."265. 

Hence  the  required  arc  is  3'  26."265. 

In  the  same  manner  we  find  the  arc  corresponding  to  logarithmic 
langent  8.184608,  to  be  0°  52'  35". 

Table  for  the  Lengths  of  Circular  Arcs,  p.  135. 

This  table  contains  the  lengths  of  every  single  degree  up  to  60,  and 
at  intervals  often  degrees  up  to  180  ;  also  for  every  minute  and  second 
up  to  20.     The  lengths  are  all  expressed  in  decimal  parts  of  radius. 

Required  the  length  of  an  arc  of  57°  17'  44ps.l 

Take  out  from  their  respective  columns  £he  lenMhs  answering  to  each 
of  these  numbers  singly,  and  add  them  afl  togemer  thus: 

57°  ....  .  /  .  0.9948377 
17'  ..../.  .0049451 
40"     .     .     ...  .0001939 

4" 0000194 

0."8 0000039 

The  sum  is         1.0000000. 

That  is,  the  length  of  an  arc  of  57°  17'  44."8  is  equal  to  the  radius  of 
the  circle. 

Traverse  Table,  pp.  136-141. 

This  table  shows  the  difference  of  latitude  and  the  departure  to  four 
decimal  places  for  distances  from  1  to  10,  and  for  bearings  from  0°  to 
90°,  at  intervals  of  15'.  If  the  bearing  is  less  than  45°,  the  angle  will 
be  found  on  the  left  margin  of  one  of  the  pages  of  the  table,  and  the  dis- 
tance at  the  top  or  bottom  of  the  page  ;  the  difference  of  latitude  will 


xvi  Explanation   of   the    Tables. 

be  found  in  the  column  headed  lat.  at  the  top  of  the  page,  and  the  de- 
parture in  the  column  headed  dep.  If  the  bearing  is  more  than  45°,  the 
angle  will  be  found  on  the  right  margin,  and  the  difference  of  latitude 
will  be  found  in  the  column  marked  lat.  at  the  bottom  of  the  page,  and 
the  departure  in  the  other  column.  The  latitudes  and  departures  for 
different  distances  with  the  same  bearing,  are  proportional  to  the  dis- 
tances. Therefore  the  distances  may  be  reckoned  as  tens,  hundreds,  or 
thousands,  if  the  place  of  the  decimal  point  in  each  departure  and  differ- 
ence of  latitude  be  changed  accordingly. 

Required  the  latitude  and  departure  for  the  distance  32.25,  and  the 
bearing  10°  30'. 

On  page  136,  opposite  to  10°  30',  we  find  the  following  latitudes  and 
departures,  proper  attention  being  paid  to  the  position  of  the  decimal 
points. 

Distance.  Dijf-  Lat.  Dep. 

30  29.498  5.467 

2  J. 96(5                         .364 

.2  197                        .036 

.05  049                        .009 


32.25  31  710  5.876. 

Table  of  Meridional   Parts,  pp.  142-148 

This  table  gives  the  length  of  the  enlarged  meridian  on  Mercator's 
Chart  to  every  minute  of  latitude  expressed  in  geographical  miles  and 
tenths  of  a  mile.  The  degrees  of  latitude  are  arranged  in  order  at  the 
top  of  the  page,  and  the  minutes  on  both  the  right  and  left  margins. 
Under  the  degrees  and  opposite  to  the  minutes  are  placed  the  merid 
onal  parts  corresponding  to  any  latitude  less  than  80°.  Thus 
the  meridional  parts  for  latitude  12°  23'  are    748.9 ; 

57°  42' are  4260.5. 

Table  op  Corrections  to  Middle  Latitude,  p.  149. 

This  table  is  used  in  Navigation  for  correcting  the  middle  latitude. 
The  given  middle  latitude  is  to  be  found  either  in  the  first  or  last  verti- 
cal column,  opposite  to  which,  and  under  the  given  difference  of  latitude, 
is  inserted  the  proper  correction  in  minutes,  to  be  added  to  the  middle 
latitude  to  obtain  the  latitude  in  which  the  meridian  distance  is  accu- 
rately equal  to  the  departure.  Thus,  if  the  middle  latitude  is  41°,  and 
the  difference  of  latitude  14°,  the  correction  will  be  found  to  be  25', 
which,  added  to  the  middle  latitude,  gives  the  corrected  middle  latitude 
41°  23' 


1 

A  TABLE 

0* 

LOGARITHMS  OF  NUMBERS 

FROM    1    TO    10,000. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

i 

2 

3 
4 
5 

6 

7 
8 

9 
io 

ii 

12 

i3 

i4 
i5 

16 

*7 

18 

*9 

20 

21 
22 
23 
24 
25 

o.oooooo 
o.3oio3o 
0.477121 
0.602060 
0.698970 

0.778151 
0.845098 
0.903090 
0.954243 
1 .000000 

1. 041393 
1 .079181 
1.113943 
1 .146128 
1 . 176091 

I .204l20 
I .23o449 
I.25527§ 
I .278754 

i .3oio3o 

1 .322219 
1.342423 
1. 361728 
1 .380211 
1.397940 

26 
27 
28 
29 
3o 

3i 

32 

33 
34 
35 

36 

37 

38 

39 
4o 

4i 
42 
43 
44 
45 

46 

47 

48 

49 

5o 

1. 4i4973 
i.43i364 
1. 447i58 
1.462398 
1 .477121 

1 .491362 
1 .5o5i5o 
i.5i85i4 
1 .53i479 
i.544o68 

i.5563o3 
1 .568202 
1.579784 
1. 591065 
1 .602060 

1. 612784 
1 .623249 
1.633468 
1.643453 
1 .6532i3 

1.662758 
1 .672098 
1.681241 
1 .690196 
1 ,698970 

5i 

52 

53 
54 
55 

56 
57 
58 
59 
60 

61 
62 
63 
64 
65 

66 
67 
68 
69 
70 

7i 

72 

73 
74 
75 

1 .707570 
1 .716003 
1.724276 
1.732394 
i.74o363 

1. 748188 
1.755875 
1.763428 
1 .770852 
i.778i5f 

i.78533o 
1.792392 
1. 79934 1 
1. 806180 
1 .812913 

1. 819544 
1 .826075 
1 .832509 
1.838849 
1.845098 

i.85i258 
1.857332 
1.863323 
1 .869232 
1. 875061 

76 

77 
78 

79 
80 

81 
82 
83 
84 
85 

86 
87 
88 
89 
90 

91 
92 

93 

94 
95 

96 
97 
98 

99 
100 

2 

880814 
886491 
892095 
897627 
903090 

908485 
9:38i4 
919078 
924279 
929419 

934498 
939519 
944483 
949390 
954243 

959041 
963788 
968483 
97312& 
977724. 

982271 
986772- 
991226 
995635 
000000 

N.B.  In  the  following  table,  the  two  leading  figures  in  the  first  column 
of  logarithms  are  to  he  prefixed  to  all  the  numbers  of  the  same  horizontal 
line  in  the  next  nine  columns ;  but  when  a  point  (.)  occurs,  its  place  is  to 
bs  supplied  by  a  cipher,  and  the  two  leading  figures  are  to  be  taken  from 
the  next  lower  line. 

A 


) 

I 

LOGARITHMS  OF  J\ 

UMII 

5  KB. 

i N 

L^o_    1 

2 

3 

4 

5 

6 

7 

8 

9 

1). 

1  xoo 

000000 1 0434 

0868 

i3oi 

1734 

2166 

2598 

3029 

346i 

3891 

43a 

IOI 

4321   475i 

5i8i 

5609 

6o38 

6466 

6894 

7321 

7748 

8174 

428 

I09 

8600  1  9026 

945i 

9876 

.3oo 

.724 

1 1 47 

l570 

r993 

24i5 

4a4 

io3 

012837  325g 

368o 

4ioo 

452i 

494o 

53Co 

5779 

6197 

6616 

419 

io4 

7o33 

745 1 

7868 

8284 

8700 

9116 

9532 

9947 

.36i 

.775 

4x6 

io5 

02 1 1 89 

i6o3 

2016 

2428 

2841 

3252 

3664 

4076 

4486 

4896 

4xa  1 

1 06 

53o6 

57i5 

6i25 

6533 

6942 

7350 

7757 

8i64 

857i 

8978 

4o8  1 

107 

9384 

9789 

.195 

.600 

ioo4 

i4o8 

1812 

2216 

2G19 

3o2I 

4o4 

108 

033424 

0826 

4227 

4628 

5029 

543o 

583o 

623o 

6629 

7028 

4oo 

109 

7426 

7825 

8223 

8620 

9017 

94i4 

9811 

.207 

.602 

•998 

396 

no 

o4i393 

1787 

2182 

2576 

2969 

3362 

3755 

4x48 

454o 

4932 

393 

in 

5323 

57i4 

6io5 

6495 

6885 

7275 

7664 

8o53 

8442 

883o 

389 

112 

9218 

9606 

9993. 

•  38o 

.766 

ii53 

i538 

1924 

2309 

2694 

386 

n3 

o53o,78m 

3463 

3846 

423o 

46 1 3 

4996 

5378 

5760 

6142 

6524 

332 

n4 

&9o5 

7286 

7666 

8o46 

8426 

88o5 

9185 

9563 

9942 

.320 

379 

n5 

060698 

1075 

i452 

1829 

2206 

c582  |  2958 

3333 

3709 

4o83 

376 

116 

4458 

4832 

5206 

558o 

5g53 

6326 

6699 

7071 

7443 

78i5 

373 

117 

8186 

8557 

8928 

9298 

9668 

..38 

.407 

.776 

u45 

i5i4 

369 

118 

07x882 

225o 

2617 

2985 

335a 

37i8 

4o85 

445 1 

4816 

5i82 

366 

119 

5547 

5912 

6276 

664o 

7004 

7368 

773i 

8094 

845  7 

8819 

363 

120 

9181 

9543 

9904 

.266 

.626 

.987 

1347 

1707 

2067 

2426 

36o 

121 

082785 

3i44 

35o3 

386i 

4219 

4576 

4934 

5291 

5647 

6oo4 

357 

N. 

0 

1 

2 

3 

4 

1   5 

6 

7 

8 

9 

IX 

r434 

r  43 

87 

i3o 

i74 

217 

260 

3o4 

347 

391 

432 

43 

86 

i3o 

x73 

216 

259 

3o2 

346 

389 

43o 

43 

86 

129 

172 

2l5 

258 

3oi 

344 

387 

428 

43 

86 

128 

171 

214 

257 

3oo 

342 

385 

426 

43 

85 

128 

r-70 

2l3 

256 

298 

34i 

383 

424 

42 

85 

127 

170 

212 

254 

297 

339 

38a 

422 

42 

84 

127 

169 

211 

253 

295 

338 

38o 

420 

42 

84 

126 

168 

2IO 

252 

294 

336 

378 

4x8 

42 

84 

125 

167 

209 

2.5l 

293 

334 

376 

4i6 

42 

83 

125 

166 

208 

25o 

291 

333 

374 

4x4 

4i 

83 

124 

166 

207 

248 

290 

33i 

373 

412 

4i 

82 

124 

i65 

206 

247 

288 

33o 

37i 

4io 

4i 

82 

123 

164 

2o5 

246 

287 

328 

369 

4o8 

4i 

83 

122 

i63 

204 

245 

286 

326 

367 

4o6 

4i' 

81 

122 

162 

203 

244 

284 

325 

365 

4o4  b 

4o 

81 

121 

1O2 

202. 

242 

283 

323 

364 

402  e3 

4o 

80 

121 

:6i 

20I 

241 

281 

322 

362 

§ 

4oo  ^ 

4o 

80 

120 

160 

200 

240 

280 

320 

36o 

Q 

Q 

398.1 

4o 

80 

II9 

1 59 

I99 

239 

279 

3i8 

358 

£  • 
p 

396"  .2  • 

4o 

79 

II9 

1 58 

I98 

238 

277 

3i7 

356 

394  | 

*9 

79  i 

rfl8 
■ki8 

i584i 

*%! 

236 

276 

3i5 

355 

392  g 

39 

78  j 

1.57 

>  196 

235 

274 

3i4 

353 

. 

390  Ph 

39 

78 

117 

1 56 

«VZ9^M 

234 

273 

3l2 

35x 

388 

39 

78 

116 

i55 

19*4  233 

272 

3io 

349 

386 

39 

77 

116 

1 54 

193 

•232 

270 

309 

347 

384 

38 

77 

1x5 

1 54 

192 

23o 

269 

307 

346 

382 

38 

76 

ii5. 

i53 

191 

229 

267 

3o6 

344 

38o 

38 

76 

ii4 

x5a 

190 

228 

266 

3o4 

342 

378 

38 

76 

ii3 

i5i 

189 

227 

265 

302 

34o 

376 

38 

75 

ix3 

i5o 

1 88 

226 

263 

3oi 

338 

374 

37 

75 

112 

i5o 

187 

224 

262 

299 

337 

372 

37 

74 

112 

i49 

186 

223 

260 

298 

335 

370 

37 

74 

in 

1 48 

i85 

222 

259 

296 

333 

368     37 

74 

110 

i47 

1 84 

221 

258 

294 

33i 

366    1  37 

73 

110 

1 46 

i83 

220 

256 

293 

329 

364     36 

73 

109 

i46 

182 

218 

255 

291 

3a8 

362     36 

72 

109 

x45 

181 

217 

a53 

290 

3a6 

36o 

{   36 

72 

108 

i44 

180 

2l6 

a5a 

288 

324 

Logarithms    of    i\  umbers. 


N.  1   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D.  ! 

I2S 

o3636o 

6716 

7071 

7426 

7781 

8i36 

8490 

8845 

9198 

9552 

355 

123 

9905 

.258 

.611 

.963 

i?i5 

1667 

2018 

2370 

2721 

3071 

35i 

124 

093422 

3772 

4l22 

4471 

4820 

5169 

55i8 

5866 

62i5 

6562 

349 

125 

6910 

7267 

76o4 

795i 

8298 

8644 

8990 

9335 

9681 

..26 

346 

126 

100371 

0715 

Io59 

i4o3 

1747 

2091 

2434 

2777 

§119 

3462 

343 

127 

38o4 

4i46 

4487 

4828 

5169 

55io 

585i 

6191 

653 1 

6871 

34 1 

128 

7210 

7549 

7888 

8227 

8565 

8903 

9241 

9579 

9916 

.253 

338 

129 

noSc^o 

0926 

1263 

1 599 

1934 

2270 

26o5 

2940 

3275 

3609 

335 

i3o 

3943 

4277 

46n 

4944 

5278 

56u 

5943 

6276 

6608 

6940 

333 

i3i 

7271 

7603 

7934 

8265 

8595 

8926 

9256 

9586 

99i5 

.245 

33o 

l32 

120574 

0903 

I23l 

i56o 

1888 

2216 

2544 

2871 

3198 

3525 

328 

i33 

3852 

4178 

45o4 

483o 

5i56 

548i 

58o6 

6i3i 

6456 

6781 

325 

1 34 

7io5 

7429 

7753 

8076 

8399 

8722 

9045 

9368 

9690 

.  .12 

323 

•35 

i3o334 

o655 

0977 

1298 

1619 

i939 

2260 

258o 

2900 

3219 

321 

i36 

3539 

3858 

4177 

4496 

48x4 

5 1 33 

545 1 

5769 

6086 

64o3 

3i8 

i37 

6721 

7037 

7354 

7671 

7987 

83o3 

8618 

8934 

9249 

9564 

3i5 

1 38 

9879 

:i94 

.5o8 

.822 

n36 

i45o 

i763 

2076 

2389 

2702 

3i4 

239 

i43oi5 

3327 

3639 

3951 

4263 

4574 

4885 

5196 

55o7 

58i8 

3n 

l4o 

6128 

6438 

6748 

7o58 

7367 

7676 

7985 

8294 

86o3 

8911 

309 

i4i 

9219 

9527 

9835 

.142 

.449 

.756 

io63 

1370 

1676 

1982 

307 

l42 

152288 

2594 

2900 

32o5 

35io 

38i5 

4l20 

4424 

4728 

5o32 

3o5 

143 

5336 

564o 

,5943 

6246 

6549 

6852 

7154 

7457 

7759 

8061 

3o3 

i44 

8362 

8664 

8965 

9266 

9567 

9868 

.168 

.469 

.769 

1068 

3oi 

i45 

i6i368 

1667 

1967 

2266 

2564 

2863 

3i6i 

346o 

3758 

4o55 

299 

146 

4353 

465o 

4947 

5244 

554i 

5838 

6i34 

643o 

6726 

7022 

297 

147 

73i7 

76i3 

7908 

8ao3 

8497 

8792 

9086 

938o 

9674 

9968 

295 

1 48 

170262 

o555 

o848 

ii4i 

i434 

1726 

2019 

23ll 

2603 

2895 

293 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

~ 9~ 

T?r 

'358 

'  36 

72 

107 

i43 

179 

2l5 

25l 

286 

322 

356 

36 

71 

107 

142 

178 

2l4 

249 

285 

320 

354 

35 

71 

106 

142 

177 

212 

248 

283 

3l9 

352 

35 

70 

106 

i4i 

176 

211 

246 

282 

3i7 

35o 

35 

70 

io5 

i4o 

,i75 

2IO 

245 

280 

3i5 

348 

35 

70 

io4 

i3g 

174 

209 

244 

278 

3i3 

346 

35 

69 

io4 

1 38 

i73 

208 

242 

277 

3n 

344 

34 

69 

io3 

1 38 

172 

206 

241 

275 

3io 

342 

34 

68 

io3 

i37 

171 

205 

239 

274 

3o8 

34o 

34 

68 

102 

1 36 

170 

204 

238 

272 

3o6 

338 

34 

68 

101 

1 35 

169 

203 

237 

270 

3o4 

336 

34 

67 

101 

1 34 

168 

202 

235 

269 

302 

334  . 

33 

67 

100 

1 34 

167 

200 

234 

267 

3oi 

332  2 

33 

66 

1 00 

i33 

166 

I99 

232 

266 

299 

03 

33o  S 

328  *z 

33 

66 

99 

1 32 

i65 

I98 

23 1 

264 

297 

O 

33 

66 

98 

i3i< 

1 64 

^6 

23o 

262 

295 

3 
2^ 

326  a  . 

0 

33 

65 

98 

i3o 

1 63 

228 

261 

293 

324  t 
0         0 

322   C. 

32 
32 

65 
64 

■W 

|t'3o 
'129 

162 
161 

194 
193 

227 

225 

259 
258 

292 
290 

320   2 

32 

64 

96 

128 

160 

192 

224 

256 

288 

3i8  ^ 

32 

64 

95 

127 

159 

191 

223 

254 

286 

3i6 

32 

63 

95 

126 

1 58 

190 

221 

253 

284 

3i4 

3i 

63 

94 

126 

i57 

188 

220 

25l 

283 

3l2 

3i 

62 

94 

125 

i56 

187 

2l8 

25o 

28: 

3io 

3i 

62 

93 

124 

i55 

186 

217 

248 

279 

3o8 

3i 

62 

92 

123 

1 54 

i85 

2l6 

246 

277 

3o6 

3i 

61 

92 

122 

i53 

184 

2l4 

245 

275 

■ 

3o4 

3o 

61 

91 

122 

l52 

.  182 

2l3 

243 

274 

302 

3o 

60 

91 

121 

i5i 

181 

211 

242 

272 

3oo 

3o 

60 

90 

120 

i5o 

180 

2IO 

240 

270 

298 

3o 

60 

89 

II9 

149 

179 

209 

238 

268 

296 

3o 

59 

89 

Il8 

1 48 

178 

207 

237 

266 

294 

29 

59 

88 

Il8 

147 

176 

206 

235 

265 

£ 

Logarithms  of  J\ 

UMBERS 

N. 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

[57 1 

1 49 

173186 

3478 

3769 

4060 

435i 

464i 

4932 

5222 

55i2 

58o2 

291 

i5o 

6091 

638i 

6670 

6959 

7248 

7536 

7825 

8n3 

84oi 

8689 

289 

i5i 

8977 

9264 

9552 

9839 

.126 

.4i3 

.699 

.986 

1272 

i558 

287 

i5a 

181844 

2129 

24i5 

2700 

2985 

3370 

3555 

383g 

4l23 

4407 

285 

i53 

4691 

4975 

5259 

5542 

5825 

6108 

6391 

6674 

6956 

7239 

283 

1 54 

7521 

7803 

8084 

8366 

8647 

8928 

9209 

9490 

9771 

..5i 

281 

i55 

190332 

0612 

0892 

1171 

i45i 

1730 

2010 

2289 

2567 

2846 

279 

i56 

3i25 

34o3 

368i 

3959 

4237 

45i4 

4792 

5069 

5346 

5623 

278 

i57 

5900 

6176 

6453 

6729 

7005 

7281 

7556 

7832 

8107 

8382 

276 

1 58 

8657 

8932 

9206 

948i 

9755 

..29 

.3o3 

.577 

•  85o 

1:24 

274 

159 

201397 

1670 

1943 

2216 

2488 

2761 

3o33 

33o5 

3577 

3848 

27a 

160 

ii2o 

439i 

4663 

4934 

5204 

5475 

5  746 

6c:6 

6286 

6556 

271 

161 

6826 

7096 

7365 

7634 

7904 

8i73 

844i 

8710 

8979 

9247 

269 

162 

q5i5 

9783 

..5i 

•  319 

.586 

.853 

1121 

i388 

1 654 

1921 

267 

i63 

212188 

2454 

2720 

2986 

3252 

35i8 

3783 

4o49 

43i4 

4579 

266 

164 

4844 

5109 

5373 

5638 

5902 

6166 

643o 

6694 

6957 

7221 

264 

i65 

7484 

7747 

8010 

8273 

8536 

8798 

9060 

9323 

9585 

9846 

262 

166 

220108 

0370 

o63i 

0892 

n53 

i4i4 

i675 

1936 

2196 

24^6 

261 

167 

2716 

2976 

3236 

3496 

3755 

4oi5 

4274 

4533 

4792 

5o5i 

259 

168 

5309 

5568 

5826 

6084 

6342 

6600 

6858 

7ii5 

7372- 

7630 

258 

169 

7887 

8i44 

84oo 

8657 

8913 

9170 

9426 

9682 

9938 

.193 

256 

170 

2 3 o449 

0704 

0960 

I2l5 

1470 

1724 

1979 

2234 

2488 

2742 

254 

171 

2996 

325o 

35o4 

3757 

4on 

4264 

45i7 

4770 

5o23 

5276 

253 

172 

5528 

578i 

6o33 

6285 

6537 

6789 

7041 

7292 

7544 

7795 

252 

i73 

8o46 

8297 

8548 

8799 

9049 

9299 

955o 

9800 

..5o 

.3oo 

25o 

174 

240549 

0799 

io48 

1297 

1 546 

i795 

2044 

2293 

254i 

2790 

249 

i75 

3o38 

3286 

3534 

3782 

4o3o 

4277 

4525 

4772 

5019 

5266 

248 

176 

55i3 

5759 

6006 

6252 

6499 

6745 

6991 

7237 

7482 

7728 

246 

177 

7973 

8219 

8464 

8709 

8954 

9198 

9443 

9687 

9932 

.176 

245 

178 

25o420 

0664 

0908 

ii5i 

1395 

i638 

1881 

2125 

2368 

2?  T> 

243 

179 

2853 

3096 

3338 

358o 

3822 

4o64 

43o6 

4548 

4790 

5o3i 

242 

180 

5273 

55i4 

5755 

5996 

6237 

6477 

6718 

6958 

7198 

7439 

241 

181 

7679 

7918 

8i58 

8398 

8637 

8877 

9116 

9355 

9594 

9833 

239 

N. 

0 

1 

0 

3 

4 

5 

6 

7 

8 

9 

D. 

'292 

'    29 

58 

88 

117 

1 46 

i75 

2o4 

234 

263 

290 

29 

58 

87 

116 

i45 

174 

203 

232 

261 

288 

29 

58 

86 

u5 

1 44 

i73 

202 

23o 

259 

286 

29 

57 

86 

n4 

i43 

172 

200 

229 

257 

284 

28 

57 

85 

n4 

142 

170 

199 

227 

256 

282 

28 

56 

85 

u3 

i4i 

169 

197 

226 

254 

280 

28 

56 

84 

112 

i4o 

168 

196 

224 

252 

278 

28 

56 

83 

in 

139 

167 

195 

223 

25o 

276 

28 

55 

83 

no 

i38 

166 

193 

221 

248 

274  a; 

27 

55 

•  82 

no 

i37 

1 64 

192 

219 

247 

272  £ 

27 

54 

82 

109 

1 36 

i63 

190 

2l8 

245 

o5 

CD 

270  ^ 

27 

54 

81 

108 

i3& 

162 

189 

2l6 

243 

a 

268  _ 

27 

54 

80 

107 

i3/f" 

161 

188 

214 

241 

£• 

266  g  • 

27 

53 

80 

106 

i33 

160 

186 

213 

239 

| 

264  « 

26 

53 

79 

106 

132 

1 58 

i85 

211 

238 

s 

262  ^ 

26 

52 

79 

io5 

i3i 

*57. 

i83 

2IO 

236 

260  P 

26 

52 

78 

io4 

i3o 

i56 

182 

208 

234 

258  £ 

26 

52 

77 

io3 

129 

i55 

181 

206 

232 

256 

26 

5i 

77 

102 

128 

i54 

x79 

2o5 

230 

254 

25 

5i 

76 

102 

127 

i5a 

178 

203 

229 

^* 

252 

25 

5o 

76 

IOI 

126 

i5i 

176 

202 

227 

25o 

25 

5o 

75 

100 

125 

i5o 

i75 

200 

225 

248 

25. 

5o 

74 

99 

124 

149 

174 

I98 

223 

246 

25 

49 

74 

98 

123 

i48 

172 

197 

221 

244 

24 

49 

73 

98 

122 

i46 

171 

195 

220 

242 

24 

48 

73 

97 

121 

145 

169 

194 

2l8 

_  ... 

240 

I  24 

48 

72 

96 

120 

i44 

168 

192 

216 

Logarithms    of    Numbers. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

I). 

238"" 

182 

260071 

o3io 

o548 

0787 

1025 

1263 

i5oi 

1739 

1976 

22l4 

i83 

245i 

2688 

2925 

3162 

3399 

3636 

3870 

4109 

4346 

4582 

2:7 

184 

4818 

5o54 

52;  V 

5525 

576i 

5996 

6232 

6467 

6702 

6937 

235 

i85 

7172 

7406 

7641 

7875 

8110 

8344 

8578 

8812 

9046 

9279 

234 

186 

g5i3 

9746 

9980 

.213 

.446 

.679 

.912 

n44 

i377 

1609 

233 

187 

271842 

2074 

23o6 

2538 

2770 

3ooi 

3233 

3464 

3696 

3927 

232 

188 

4i58 

4389 

4620 

485o 

5o8i 

53n 

5542 

5772 

6002 

6232 

23o 

189 

6462 

6692 

6921 

7i5: 

7380 

7609 

7838 

8067 

8296 

8525 

229 

190 

8754 

8982 

9211 

9439 

9667 

9895 

.123 

.35i 

.578 

.806 

228 

I9I 

28io33 

1261 

i488 

1 71 5 

1942 

2169 

2396 

2622 

2849 

3075 

227 

392 

33oi 

3527 

3753 

3979 

42o5 

443 1 

4656 

4882 

5107 

5332 

226 

193 

5557 

5782 

6007 

6232 

6456 

6681 

6905 

7i3o 

7354 

7578 

225 

194 

7802 

8026 

8249 

8473 

8696 

8920 

9i43 

9366 

9589 

9812 

223 

195 

290035 

0257 

0480 

0702 

0925 

n47 

i36g 

1591 

i8i3 

2034 

222.. 

I96 

2256 

2478 

2699 

2920 

3i4i 

3363 

3584 

38o4 

4025 

4246 

221 

I97 

4466 

4687 

4907 

5127 

5347 

5567 

5787 

6007 

6226 

6446 

220 

I98 

6665 

6884 

7104 

7323 

7542 

7761 

7979 

8198 

8416 

8635 

219 

I99 

8853 

9071 

9289 

95o7 

9725 

9943 

.161 

•  378 

.595 

.8i3 

2l8 

200 

3oio3o 

1247 

i464 

1681 

1898 

2Il4 

233i 

2547 

2764 

2980 

217 

20I 

319.6 

3412 

3628 

3844 

4059 

4275 

4491 

4706 

4921 

5i36 

2l6 

202 

535i 

5566 

578i 

5996 

6211 

6425 

6639 

6854 

7068 

7282 

2l4 

203 

7496 

7710 

7924 

8i37 

835i 

8564 

8778 

8991 

9204 

9417 

2l3 

204 

9630 

9843 

..56 

.268 

.481 

.693 

.906 

1118 

i33o 

1 542 

212 

205 

3i 1 764 

1966 

21 77 

2389 

2600 

2812 

3o23 

3234 

3445 

3656 

211 

206 

3867 

4078 

4289 

4499 

4710 

4920 

5i3o 

534o 

555i 

5760 

2lO 

207 

5970 

6180 

6390 

6599 

6809 

7018 

7227 

7436 

7646 

7854 

209 

208 

8o63 

8272 

848 1 

8689 

8898 

9106 

93i4 

9522 

973o 

9938 

208 

SO9 

32oi46 

o354 

o562 

0769 

0977 

1184 

1391 

1598 

i8o5 

2012 

207 

2IO 

2219 

2426 

2633 

2839 

3o46 

3252 

3458 

3665 

387i 

4077 

2o6 

211 

4282 

4488 

4694 

4899 

5io5 

53io 

55i6 

5721 

5926 

6i3i 

205 

212 

6336 

654i 

6745 

6950 

7i55 

7359 

7563 

7767 

7972 

8176 

204 

213 

838o 

8583 

8787 

8991 

9i94 

9398 

9601 

9805 

...8 

.211 

203 

si4 

33o4i4 

0617 

0819 

1022 

1225 

1427 

i63o 

i832 

2034 

2236 

202. 

2l5 

2438 

264c 

2842 

3o44 

3246 

3447 

3649 

385o 

4o5i 

4253 

202 

316 

4454 

4655 

4856 

5o57 

5257 

5458 

5658 

5859 

6o5g 

6260 

20I 

217 

646o 

6660 

6860 

7060 

7260 

7459 

7659 

7858 

8o58 

8257 

200 

218 

8456 

8656 

8855 

9054 

9253 

945 1 

965o 

9849 

..47 

.246 

I99 

219 

34o444 

0642 

084V 

1039 

1237 

i435 

i632 

i83o 

2028 

2225 

I98 

220 

2423 

2620 

2817 

3oi4 

3212 

3409 

36o6 

38o2 

3999 

4l96 

I97 

N.  |   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

238 

'  24 

48 

71 

95 

119 

i43 

167 

190 

214 

236 

24 

47 

71 

94 

118 

142 

i65 

189 

212 

234 

23 

47 

70 

94 

117 

i4o 

1 64 

187 

211 

232 

2J 

46 

70 

93 

116 

139 

162 

186 

209 

23o 

23 

46 

69 

92 

n5 

i38 

1 61 

1 84 

207 

228 

23 

46 

68 

91 

n4 

i37 

160 

182 

2o5 

226 

23 

45 

68 

90 

n3 

i36 

i58 

181 

2o3 

224  2 

22 

45 

67 

90 

112 

1 34 

i57 

179 

202 

• 

222  ce 

22 

44 

67 

89 

in 

i33 

i55 

178 

200 

0 
c 

220  " 

82 

44 

66 

88 

no 

l32 

1 54 

176 

198 

®  1     a 
SI  218  .2* 

22 

44 

65 

87 

109 

i3i 

i53 

174 

196 

5 

216  fe 

22 

43 

65 

86 

108 

i3o 

i5i 

i73 

194 

"   2l4   §" 

21 

43 

64 

86 

107 

128 

i5o 

171 

193 

212  p^ 

21 

42 

64 

85 

106 

127 

1 48 

170 

191 

210 

21 

42 

63 

84 

io5 

126 

147 

168 

189 

208 

21 

42 

62 

83 

104 

125 

i46 

166 

187 

206 

11 

4i 

62 

82 

io3 

124 

1 44 

1 65 

i85 

204 

20 

4i 

61 

82 

102 

122 

i43 

i63 

1 84 

202 

20 

4o 

61 

81 

101 

121 

141 

162 

182 

_  1 

200 

20 

4o 

60 

80 

100  . 

120 

i4o 

160 

180 

r98 

20 

4o 

59 

79 

99 

I!9 

1 39 

i58 

178 

1 

c 

Logarithms  < 

)F  JN 

OMBERS 

1 

N.    0 

1 

2 

3 

4 

5 

6 

7 

1  8 

9 

D. 

221 

344392 

4589 

4785 

4981 

5i78 

5374 

5570 

5766 

5962 

6:57 

196 

222 

6353 

6549 

6744 

6939 

7i35 

733o 

7525 

7720 

79i5 

8:10 

i95 

223 

83o5 

85oo 

8694 

8889 

9083 

9278 

9472 

9666 

9860 

..54 

i94 

224 

35o248 

o442 

o636 

0829 

I023 

1216 

i4io 

i6o3 

1796 

1989 

i93 

225 

2i83 

2375 

2568 

2761 

2954 

3i47 

3339 

3532 

3724 

3qi6 

£26 

4io8 

43oi 

4493 

4685 

4876 

5o68 

5260 

5452 

5643 

5834 

192 

227 

6026 

6217 

64o8 

6599 

6790 

6981 

7172 

7363 

7554 

7744 

191 

228 

7935 

8i25 

83i6 

85o6 

8696 

8886 

9076 

9266 

9456 

9646 

190 

229 

9835 

..25 

•  2l5 

•  4o4 

.593 

•  783 

.972 

1161 

i35o 

1539 

189 

23o 

361728 

1917 

2io5 

2294 

2482 

2671 

2859 

3o48 

3236 

3424 

188 

23: 

36i2 

38oo 

3988 

4176 

4363 

455i 

4739 

4926 

5n3 

53oi 

232 

5488 

5675 

5862 

6049 

6236 

6423 

6610 

6796 

6983 

7169 

187 

233 

7356 

7542 

7729 

79i5 

8101 

8287 

8473 

8659 

8845 

9o3o 

186 

234 

9216 

9401 

9587 

9772 

9958 

.i43 

.328 

•  5i3 

.698 

.883 

i85 

235 

371068 

1253 

i437 

1622 

1806 

1991 

2175 

236o 

2544 

2728 

1 84 

236 

2912 

3096 

3280 

3464 

3647 

383i 

4oi5 

4198 

4382 

4565 

237 

4748 

4932 

5u5 

5298 

548i 

5664 

5846 

6029 

6212 

6394 

i83 

238 

6577 

6759 

6942 

7124 

7306 

7488 

7670 

7852 

8o34 

8216 

182 

239 

8398 

858o 

8761 

8943 

9124 

9306 

9487 

9668 

9849 

..3o 

181 

240 

380211 

0392 

0573 

0754 

0934 

iii5 

1296 

1476 

i656 

i837 

241 

2017 

2197 

2377 

2557 

2737 

2917 

3o97 

3277 

3456 

3636 

180 

242 

38i5 

3995 

4x74 

4353 

4533 

4712 

489i 

5070 

5249 

5428 

179 

243 

56o6 

5785 

5964 

6142 

632i 

6499 

6677 

6856 

7034 

7212 

178 

a44 

739° 

7568 

7746 

7923 

8101 

8279 

8456 

8634 

8811 

8989 

245 

9166 

9343 

9520 

9698 

9875 

..5i 

.228 

.4o5 

.582 

•759 

177 

246 

390935 

1112 

1288 

i464 

1 64 1 

1817 

i993 

2169 

2345 

2521 

176 

247 

2697 

2873 

3o48 

3224 

34oo 

3575 

375i 

3926 

4ioi 

4277 

248 

4452 

4627 

4802 

4977 

5i52 

5326 

55oi 

5676 

585o 

6025 

i75 

249 

6199 

6374 

6548 

6722 

6896 

7071 

7245 

7419 

7592 

7766 

i74 

25o 

7940 

8n4 

8287 

8461 

8634 

8808 

8981 

9154 

9328 

95oi 

i73 

»5i 

9674 

9847 

.  .20 

.192 

.365 

.538 

.711 

.883 

io56 

1228 

252 

4oi4oi 

i573 

1745 

1917 

2089 

2261 

2433 

26o5 

2777 

2949 

172 

253 

3l2I 

3292 

3464 

3635 

3807 

3978 

4i4g 

432o 

4492 

4663 

I71 

254 

4834 

5oo5 

5176 

5346 

55i7 

5688 

5858 

6029 

6199 

6370 

255 

654o 

6710 

6881 

7o5i 

7221 

739i 

756i 

773i 

7901 

S070 

t7o 

256 

8240 

84io 

8579 

8749 

8918 

9087 

9257 

9426 

9595 

9764 

169 

257 

9933 

.  102 

.271 

•  44o 

.609 

•777 

.946 

1 1 1 4 

1283 

i45i 

258 

4i 1620 

1788 

1956 

2124 

2293 

2461 

2629 

2796 

2964 

3i32 

168 

259 

33oo 

3467  3635 

38o3 

397o 

4i37 

43o5 

4472 

4639 

4806 

167 

260 

4973 

5i4o  5307 

5474 

564i 

58o8 

5974 

6i4i 

63o8 

6474 

261 

664 1 

6807  ■  6973 

7i39 

7306 

7472 

7638 

7804 

7970 

8i35 

1 66 

262 

83oi 

6467  !  8633 

8798 

8964 

9129 

9295 

9460 

9625 

9791 

i65 

263 

9956 

.121   .286 

.45i 

.616 

.781 

.945 

mo 

1275 

1439 

N. 

G 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

"196    f  20 

39 

59 

78 

98 

118 

i37 

r57 

176 

i94 

J9 

39 

58 

78 

97 

no 

i36 

i55 

i75 

:92 

l9 

38 

58 

77 

96 

n5 

1 34 

1 54 

i73 

190 

*9 

38 

57 

76 

95 

u4 

1 33 

l52 

171 

188 

J9 

38 

56 

75 

94 

n3 

i3a 

i5o 

:69 

186  2 

J9 

37 

56 

74 

93 

1 12 

i3o 

149 

167 

op 

8 

c 

i84  f2 

18 

3? 

55 

74 

92 

no 

•  129 

147 

166 

182  -3 

18 

36 

55 

73 

91 

109 

127 

i46 

1 64 

2- 

180  §< 

18 

36 

54 

72 

90 

108 

126 

1 44 

162 

£ 

178  s 

18 

36 

53 

71 

89 

107 

125 

142 

160 

p 

176  a 

18 

35 

53 

70 

88 

106 

123 

i4i 

i58 

174 1 
172 

17 

35 

52 

70 

87 

104 

122 

139 

i57 

*7 

34 

52 

69 

86 

io3 

I20 

i38 

i55 

170 

17 

34 

5i 

68 

85 

102 

119 

i36 

i53 

168 

*7 

34 

5o 

67 

84 

101 

Il8 

1 34 

i5i 

166 

17 

33 

5o 

66 

83 

100 

Il6 

i33 

149 

Li64 

16 

33 

49 

66 

8, 

98 

n5 

i3i 

1 48 

Logarithms 

OF  N 

UMBERS. 

\ 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

I). 

264 

421604 

1768 

1933 

2097 

2261 

2426 

2590 

2754 

2918 

3082 

1 64 

a65 

3246 

3410 

3574 

3737 

3901 

4o65 

4228 

4392 

4555 

4718 

266 

4882 

5o45 

5208 

537i 

5534 

5697 

586o 

6023 

6186 

6349 

i63 

267 

65n 

6674 

6836 

6999 

7161 

7324 

7486 

7648 

7811 

7973 

163 

268 

8i35 

8297 

8459 

8621 

8783 

8944 

9106 

9268 

9429 

959i 

269 

9752 

9914 

..75 

.236 

.398 

.559 

.720 

.881 

1042 

I203 

i6f 

270 

43i364 

i525 

i685 

1 846 

20Q7 

2167 

2328 

2488 

2649 

2809 

£71 

2969 

3i3o 

3290 

345o 

36 10 

377o 

3930 

4090 

4249 

4409 

160 

272 

4569 

4729 

4888 

5o48 

5207 

5367 

5526 

5685 

5844 

6oo4 

i5g 

273 

6i63 

6322 

648 1 

664o 

6799 

6957 

7116 

7275 

7433 

7592 

274 

775i 

7909 

8067 

8226 

8384 

8542 

8701 

8859 

9017 

9175 

i58 

275 

9333 

9491 

9648 

9806 

9964 

.  122 

.279 

.437 

•  594 

.752 

276 

440909 

1066 

1224 

i38i 

i538 

1695 

i852 

2009 

2166 

2323 

i57 

277 

2480 

2637 

2793 

2950 

3io6 

3263 

3419 

3576 

3732 

3889 

278 

4o45 

4201 

4357 

45i3 

4669 

4825 

4981 

5i37 

5293 

5449 

1 56 

279 

56o4 

5760 

5915 

6071 

6226 

6382 

6537 

6692 

6848 

7003 

i55 

280 

7i58 

73i3 

7468 

7623 

7778 

7933 

8088 

8242 

8397 

8552 

281 

8706 

8861 

9015 

9170 

9324 

9478 

9633 

9787 

994i 

..95 

i54 

282 

450249 

o4o3 

o557 

0711 

o865 

1018 

1172 

i326 

J479 

i633 

283 

1786 

1940 

2093 

2247 

2400 

2553 

2706 

2859 

3012 

3i65 

i53 

284 

33i8 

347i 

3624 

3777 

3930 

4082 

4235 

4387 

4540 

4692 

285 

4845 

4997 

5i5o 

53o2 

5454 

56o6 

5758 

5910 

6062 

6214 

l52 

286 

6366 

65i8 

6670 

6821 

6973 

7125 

7276 

7428 

7579 

773i 

287 

7882 

8o33 

8i84 

8336 

8487 

8638 

8789 

8940 

9091 

9242 

i5i 

288 

9392 

9543 

9694 

9845 

9995 

.i46 

.296 

•  447 

.597 

•  748 

289 

460898 

1048 

1198 

1 348 

1 499 

1649 

1799 

1948 

2098 

2248 

i5o 

390 

2398 

2548 

2697 

2847 

2997 

3i46 

3296 

3445 

3594 

3744 

29: 

3893 

4042 

4191 

434o 

4490 

463g 

4788 

4936 

5o85 

5234 

i49 

292 

5383 

5532 

568o 

5829 

5977 

6126 

6274 

6423 

657i 

6719 

1 

293 

6868 

7016 

7164 

73i2 

7460 

7608 

7756 

7904 

8o52 

8200 

1 48 

294 

8347 

8495 

8643 

8790 

8938 

9085 

9233 

9380 

9527 

9675 

295 

9822 

9969 

.116 

.263 

.410 

.557 

.704 

.85.1 

.998 

1 145 

147 

296  471292 

i438 

i585 

1732 

1878 

2025 

2171 

23i8 

2464 

2610 

297 

2756 

2903 

3o49 

3195 

334i 

3487 

3633 

3779 

3925 

4071 

i46 

298 

4216 

4362 

45o8 

4653 

4799 

4944 

5090 

5235 

538i 

5526 

299 

5671 

58i6 

5962 

6107 

6252 

6397 

7844 

6542 

6687 

6832 

6976 

i45 

3oo 

7121 

7266 

741 1 

7555 

7700 

7989 

8i33 

S278 

8422 

3oi 

8566 

8711 

8855 

8999 

9i43 

9287 

943i 

9575 

9719 

9863 

1 44 

302 

480007 

oi5i 

020  4 

o438 

o582 

0725 

0869 

1012 

n56 

1299 

3o3 

i443 

x58o 

1729 

1872 

2016 

2159 

2302 

2445 

2588 

2731 

i43 

3o4 

2874 

3oi6 

3i5g 

33o2 

3445 

3587 

3730 

3872 

4oi5 

4i57 

3o5 

43oo . 

4442 

4585 

4727 

4869 

5on 

5i53 

5295 

5437 

5579 

i4a 

3o6 

5721 

5863 

6oo5 

6i47 

6289 

643o 

6572 

6714 

6855 

6997 

307 

7i38 

7280 

7421 

7563 

7704 

7845 

7986 

8127 

8269 

84io 

141 

3o8 

855i 

8692 

8833 

8974 

9114 

9255 

9396 

9537 

9677 

9818 

309 

9958 

••99 

.239 

.38o 

.520 

.661 

.801 

•  94i 

1081 

1222 

140 

3io 

491362 

l502 

1642 

1782 

1922 

2062 

2201 

234l 

2481 

2621 

3n 

2760 

2900 

3o4o 

3i79 

33ig 

3458 

3597 

3737 

3876 

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3837 

3955 

4074 

4192 

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4429 

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116 

374 

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108 

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3253 

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3469 

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5628 

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5844 

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6059 

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6489 

6596 

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6160 

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7366 

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429 

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3872 

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1970 

2069 

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1827 

1899 

1971 

2042 

2Il4 

2186 

2258 

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2401 

606 

2473 

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2616 

2688 

2759 

283i 

2902 

2974 

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3117 

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3i89 

3260 

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3832 

71 

608 

39o4 

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4261 

4332 

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4546 

609 

4617 

4689 

4760 

483i 

4902 

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610 

533o 

54oi 

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5757 

5828 

5899 

5970 

611 

6o4i 

6112 

6i83 

6254 

6325 

6396 

6467 

6538 

6609 

6680 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

77  » 

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23 

3i 

39 

46 

54 

62 

69 

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CO 

76  e 

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Logarithms 

J  F  i\ 

IT  iM  B  E  R  S. 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

9 

D. 

71 

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8027 

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614 

8168 

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9016 

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9i57 

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9369 

944o 

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616 

958i 

965i 

9722 

9792 

9863 

9933 

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•  i44 

.215 

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617 

790285 

o356 

0426 

0496 

0567 

0637 

0707 

0778 

0848 

0918 

618 

0988 

1059 

1129 

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1269 

1 340 

i4io 

i48o 

i55o 

1620 

619 

1691 

1761 

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1901 

1971 

2o4l 

2111 

2181 

2252 

2322 

620 

2392 

2462 

2532 

2602 

2672 

2742 

0812 

2882 

2952 

3022 

621 

3092 

3i62 

323i 

33oi 

337i 

344l 

35n 

358i 

365i 

3721 

1  622 

3790 

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3930 

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4070 

4i39 

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4279 

4349 

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4488 

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4906 

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5254 

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5463 

5532 

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574i 

58n 

625 

588o 

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6019 

6088 

6i58 

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6297 

6366 

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69 

626 

6574 

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67i3 

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6921 

6990 

7060 

7129 

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627 

7268 

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7683 

7752 

7821 

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628 

7960 

8029 

8098 

8167 

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865i 

8720 

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8858 

8927 

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9065 

9134 

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9823 

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0717 

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0923 

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1061 

1129 

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633 

i4o4 

1472 

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1609 

1678 

1747 

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1 884 

1952 

2021 

634 

2089 

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2568 

2637 

2705 

635 

2774 

2842 

2910 

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3o47 

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3252 

332i 

3389 

68 

636 

3457 

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3730 

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4139 

4208 

4276 

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6519 

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6723 

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6858 

6926 

6994 

7061 

7129 

7197 

7264 

7332 

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7467 

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7535 

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7738 

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4647 

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4780 

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66 

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6639 

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7169 

7235 

7301 

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657 

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8028 

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1906 

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2037 

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65 

664 

2168 

2233 

2299 

2364 

2430 

2495 

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2626 

2691 

2756 

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N. 

0 

1 

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3 

4 

5 

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7 

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9 

71  » 

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14 

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28 

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57 

64 

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27 

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67  S 

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60 

P 

66  g 

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20 

26 

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LOGARH 

HMS 

OF  N 

UMBERS. 

11 

N. 

0 

1 

2 

3 

4 

1 
5 

6 

7 

8 

9 

D. 

665 

822822 

2887 

2952 

3oi8 

3o83 

3i48 

32i3 

3279 

3344 

3409 

65 

666 

3474 

3539 

36o5 

3670 

3735 

38oo 

3865 

3930 

3996 

4o6i 

667 

4126 

4191 

4256 

432i 

4386 

445 1 

45i6 

458i 

4646 

4711 

668 

4776 

484i 

4906 

4971 

5o36 

5ioi 

5i66 

523i 

5296 

536i 

669 

5426 

5491 

5556 

562i 

5686 

575i 

58i5 

,588o 

5945 

6010 

670 

6075 

6i4o 

6204 

6269 

6334 

6399 

6464 

6528 

6593 

6658 

671 

6723 

6787 

6852 

6917 

6981 

7046 

7111 

7i75 

7240 

73o5 

672 

7369 

7434 

7499 

7563 

7628 

7692 

7757 

7821 

-7886 

795i 

673 

8oi5 

8o'8o 

8i44 

8209 

8273 

8338 

8402 

8467 

853i 

8595 

64 

674 

8660 

8724 

8789 

8853 

8918 

8982 

9046 

9111 

9175 

9239 

675 

93o4 

936? 

9432 

9497 

9561 

9625 

9690 

9754 

9818 

9882 

676 

9947 

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.  139 

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677 

83o589 

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0717 

0781 

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1037 

1 1 02 

1166 

678 

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1294 

i358 

1422 

i486 

i55o 

1614 

1678 

1742 

1806 

679 

1870 

1934 

1998 

2062 

2126 

2189 

2253 

2317 

238i 

2445 

680 

2509 

2573 

2637 

2700 

2764 

2828 

2S92 

2956 

3020 

3o83 

681 

3i47 

3211 

3275 

3338 

3402 

3466 

353o 

35g3 

3657 

3721 

682 

3784 

3848 

3912 

3975 

4039 

4io3 

4i66 

423o 

4294 

4357 

683 

442i 

4484 

4548 

46n 

4675 

4739 

4802 

4866 

4929 

4993 

684 

5o56 

5l20 

5i83 

5247 

53io 

5373 

5437 

55oo 

5564 

5627 

63 

685 

5691 

5754 

58i7 

588i 

5944* 

6007 

6071 

6:34 

6197 

6261 

686 

6324 

638  7 

645i 

65i4 

6577 

664i 

6704 

6767 

683o 

6894 

687 

6957 

7020 

7083 

7146 

7210 

7273 

7336 

7399 

7462 

7525 

688 

7588 

7652 

77i5 

7778 

784i 

79°4 

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8o3o 

8o93 

8i56 

689 

82m 

8282 

8345 

84o8 

8471 

8534 

8597 

8660 

8723 

8786 

690 

8849 

8912 

8975 

9o38 

9101 

9164 

9227 

9289 

9352 

94i5 

691 

9478 

9541 

9604 

9667 

9729 

9792 

9855 

9918 

9981 

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692 

84oio6 

0169 

0232 

0294 

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0420 

0482 

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0608 

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693 

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0921 

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1046 

1 1 09 

1 1 72 

1234 

1297 

694 

1359 

1422 

i485 

i547 

1610 

1672 

1735 

1797 

i860 

1922 

695 

1985 

2047 

2110 

2172 

2235 

2297 

236o 

2422 

2484 

2547 

62 

696 

2609 

2672 

2734 

2796 

2859 

2Q2I 

2983 

3o46 

3io8 

3170 

697 

3233 

3295 

3357 

3420 

3482 

3544 

3Co6 

3669 

373i 

3793 

698 

3855 

39i8 

3980 

4042 

4io4 

4166 

4229 

4291 

4353 

44i5 

699 

4477 

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4726 

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485o 

4912 

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5o36 

700 

5o98 

5i6o 

5222 

5284 

5346 

5408 

5470 

5532 

5594 

5656 

701 

57i8 

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5842 

5904 

5966 

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6399 

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6523 

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6770 

6832 

6894 

703 

6955 

7017 

7079 

7141 

7202 

7264 

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7449 

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704 

7573 

7634 

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8o<?4 

8066 

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8189 

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83i2 

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8435 

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8559 

8620 

8682 

8743 

706 

88o5 

8866 

8928 

8989 

9o5i 

9112 

9174 

9235 

9297 

9358 

61 

707 

9419 

948i 

9S42 

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9665 

9726 

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9849 

991 1 

9972 

708 

85oo33 

0096 

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0217 

0279 

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0462 

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709 

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0952 

1014 

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1197 

710 

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1625 

1686 

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1809 

711 

1870 

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1992 

2o53 

2114 

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2297 

2358 

2419 

712 

2480 

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2602 

2663 

2724 

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2846 

2907 

2968 

3029 

71.3 

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3i5o 

3211 

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3333 

3394 

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35i6 

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714 

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388i 

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4002 

4o63 

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6124 

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6548 

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6668 

60 

719 

6729 

6789 

685o 

6910 

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7o3i 

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7212 

7272 

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0 

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64  £  {     6 
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16 


Logarithms   of   Numbers. 


720 

0 

1 

2 

3 

4 

5    6 

7 

8 

9 

D. 

857332 

7393 

7453 

75i3 

7574 

7634 

7694 

7755 

78i5 

7875 

60 

721 

7935 

7995 

8o56 

8116 

8176 

8236 

8297 

8357 

8417 

8477 

722 

8537 

8597 

8657 

8718 

8778 

8838 

8898 

8958 

9018 

9078 

723 

9i38 

9198 

9258 

9318 

9379 

9439 

9499 

9.559 

9619 

9679 

724 

9739 

9799 

9859 

9918 

9978 

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..98 

.158 

.218 

.278 

725 

S6o338 

0398 

o458 

o5i8 

0578 

0637 

0697 

0757 

0817 

0877 

726 

o937 

0996 

io56 

1116 

1 1 76 

1236 

1295 

i355 

i4i5 

i475 

727 

i534 

1 S94 

i654 

1714 

i773 

i833 

1893 

1952 

2012 

2072 

728 

2l3l 

2191 

225l 

23lO 

2370 

243o 

2489 

2549 

2608 

2668 

729 

2728 

2787 

2847 

2906 

2966 

3o25 

3o85 

3i44 

3204 

3263 

73o 

33s3 

3382 

3442 

35oi 

356i 

3620 

368o 

3739 

3799 

3858 

59 

73i 

3917 

3977 

4o36 

4096 

4i55 

4214 

4274 

4333 

4392 

4452 

732 

45n 

4570 

463o 

4689 

4748 

48o8 

4867 

4926 

4985 

5  o45 

733 

5io4 

5i63 

5222 

5282 

534i 

54oo 

5459 

5S19 

5578 

5637 

734 

5696 

5755 

58i4 

5874 

5933 

5992 

6o5i 

6110 

6169 

6228 

735 

6287 

6346 

64o5 

6465 

6524 

6583 

6642 

6701 

6760 

6819 

736 

6878 

6937 

6996 

7o55 

7114 

7173 

7232 

7291 

7350 

7409 

737 

7467 

7526 

7585 

7644 

77°3 

7762 

7821 

7880 

7939 

7998 

738 

8o56 

8n5 

8i74 

8233 

8292 

835o 

8409 

8468 

8527 

8586 

739 

8644 

87o3 

8762 

8821 

8879 

8938 

8997 

9o56 

9114 

9i73 

74o 

9232 

9290 

9349 

9408 

9466 

9525 

9584 

9642 

9701 

9760 

741 

9818 

9877 

993S 

9994 

..53 

.111 

.170 

.228 

.287 

.345 

742 

870404 

0462 

o52I 

o579 

o638 

0696 

0755 

o8i3 

0872 

0930 

58 

743 

0989 

1047 

1106 

1164 

1223 

1281 

i33g 

i3g8 

i456 

i5i5 

744 

i573 

i63i 

1690 

1 748 

1806 

i865 

1923 

1981 

2b4o 

2098 

745 

2i56 

22l5 

2273 

233i 

238g 

2448 

25o6 

2564 

2622 

2681 

746 

2739 

2797 

2855 

2913 

2972 

3o3o 

3o88 

3i46 

3204 

3262 

747 

332i 

3379 

343? 

3495 

3553 

36n 

3669 

3727 

3785 

3844 

748 

3902 

3960 

4oi8 

4076 

4i34 

4192 

425o 

43o8 

4366 

4424 

749 

4482 

4540 

4598 

4656 

4714 

4772 

483o 

4888 

4945 

5oo3 

75o 

5o6i 

5119 

5i77 

5235 

5293 

535i 

5409 

5466 

5524 

5582 

75i 

564o 

5698 

5756 

58i3 

587i 

5929 

5987 

6o45 

6102 

6160 

752 

6218 

6276 

6333 

6391 

6449 

6507 

6564 

6623 

6680 

6737 

753 

6795 

6853 

6910 

6968 

7026 

7083 

7*4i 

7199 

7256 

73i4 

754 

7371 

7429 

7487 

7544 

7602 

7659 

7717 

7774 

7832 

7889 

755 

7947 

8oo4 

8062 

8119 

8177 

8234 

8292 

8349 

8407 

8464 

57 

756 

8522 

8579 

8637 

8694 

8752 

8809 

8866 

8924 

8981 

9039 

757 

9096 

9i53 

9211 

9268 

9325 

9383 

944o 

9497 

9555 

9612 

758 

9669 

9726 

9784 

9841 

9898 

9956 

..i3 

..70 

.127 

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3363 

34 1.0 

3457 

35o4 

3552 

3599 

3646 

36g3 

374l 

920 

3788 

3835 

3882 

3929 

3977 

4024 

4071 

4n8 

4i65 

4212 

921 

4260 

4307 

4354 

44oi 

4448 

4495 

4542 

4590 

4637 

4684 

922 

473i 

4?78 

4825 

4872 

4919 

4966 

5oi3 

5o6i 

5io8 

5i55 

923 

5202 

5249 

5296 

5343 

5390 

5437 

5484 

553i 

5578 

5625 

924 

5672 

57i9 

5766 

58i3 

586o 

5907 

5954 

6001 

6o48 

6095 

925 

6l42 

6189 

6236 

6283 

6329 

6376 

6423 

6470 

65i7 

6564 

926 

6611 

6658 

6705 

6752 

6799 

6845 

6892 

6939 

6986 

7o33 

927 

7080 

7127 

7i73 

7220 

7267 

73i4 

736i 

7408 

7454 

75oi 

928 

7548 

7595 

7642 

7688 

7735 

7782 

7829 

7875 

7922 

7969 

929 

8016 

8062 

8109 

8i56 

8203 

8249 

8296 

8343 

839o 

8436 

930 

8483 

853o 

8576 

8623 

8670 

8716 

8763 

8810 

8856 

89o3 

931 

895o 

8996 

9043 

9090 

9i36 

9183 

9229 

9276 

9323 

9369 

932 

9416 

9463 

9509 

9556 

9602 

9649 

9695 

9742 

9789 

9835 

933 

9882 

9928 

9975 

.  .21 

..68 

.114 

.161 

.207 

.254 

•  3oo 

934 

970347 

0393 

o44o 

o486 

o533 

o579 

0626 

0672 

0719 

076S 

46 

935 

0812 

o858 

0904 

0951 

0997 

io44 

1090 

1 137 

n83 

1229 

936 

1276 

l322 

1369 

i4i5 

i46i 

i5o8 

i554 

1601 

1647 

1693 

937 

1740 

I786 

i832 

1879 

1925 

1971 

2018 

2064 

2110 

2157 

g38 

2203 

2249 

2295 

2342 

2388 

2434 

2481 

2527 

2573 

2619 

939 

2666 

2712 

2758 

2804 

285i 

2897 

2943 

2989 

3o35 

3082 

940 

3128 

3i74 

3220 

3266 

33i3 

3359 

34o5 

345i 

3497 

3543 

941 ! 

3590 

3636 

3682 

3728 

3  7  74 

3820 

3866 

3913 

3959 

4oo5 

942 1 

4o5i  4097 

4i43 

4i89 

42  35 

4281 

4327 

4374 

4420 

4466 

94-3| 

45i2  1  4558 

46o4 

465o 

4696 

4742 

4788 

4834 

488o 

4926 

D. 

NT[ 

0     1 

2 

3 

4   1 

5 

6 

7 

8 

9 

c  ( 
* 

■  49  »  f  5 

47  5-i  \      5 

10 

i4 

r9 

24 

29 

34 

38 

43 

9 

i4 

J9 

24- 

28 

33 

38 

42 

P  1 

46  pi  I  5 

9 

:4 

18 

23 

28 

32 

37 

4i 

20 

Logarithms 

UF   N 

UMB 

ERS. 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9  [  Ii 

944 

974972 

5oi8 

5o64 

5no 

5i56 

5202 

5248 

5294 

534o 

5386 

46 

945 

5432 

5478 

5524 

5570 

56i6 

5662 

57o7 

5753 

5799 

5845 

946 

5891 

5937 

5983 

6029 

6075 

6121 

6167 

6212 

6258 

63o4 

947 

635o 

6396 

6442 

6488 

6533 

6579 

6625 

6671 

6717 

6763 

949 

6808 

6854 

6900 

6946 

6992 

7o37 

7083 

7129 

7i75 

7220 

949 

7266 

73i2 

7358 

74o3 

7449 

7495 

754i 

7586 

7632 

7678 

q5c 

7724 

7769 

78i5 

7861 

7906 

7952 

7998 

8o43 

8089 

8i35 

95i 

8181 

8226 

8272 

83i7 

8363 

8409 

8454 

85oo 

8546 

859i 

952 

8637 

8683 

8728 

8774 

8819 

8865 

891 1 

8956 

9002 

9047 

953 

9093 

9i38 

9184 

9230 

9275 

9321 

9366 

9412 

9457 

95o3 

954 

9548 

9594 

9639 

9685 

973o 

9776 

9821 

9867 

9912 

9958 

955 

980003 

0049 

0094 

oi4o 

oi85 

023l 

0276 

o322 

0367 

o4l2 

45 

956 

o458 

o5o3 

0549 

0594 

o64o 

o685 

0730 

O776 

0821 

0867 

957 

0912 

°957 

ioo3 

io48 

1093 

1139 

1184 

I229 

1275 

l320 

9  58 

i366 

i4n 

i456 

i5oi 

1 547 

1592 

i637 

i683 

1728 

1773 

959 

1819 

1864 

1909 

1954 

2000 

2o45 

2090 

2i35 

2181 

2226 

960 

2271 

23i6 

2362 

2407 

2452 

2497 

2543 

2588 

2633 

2678 

961 

2723 

2769 

2814 

285g 

2904 

2949 

2994 

3o4o 

3o85 

3i3o 

962 

3i75 

3220 

3265 

33io 

3356 

34oi 

3446 

3491 

3536 

358i 

963 

3626 

367i 

37i6 

3762 

3807 

3852 

3897 

3942 

3987 

4o32 

964 

4077 

4l22 

4167 

4212 

4257 

4302 

4347 

4392 

4437 

4482 

965 

4527 

4572 

4617 

4662 

4707 

4752 

4797 

4842 

4887 

4932 

966 

4977 

5022 

5067 

5lI2 

5i57 

5202 

5247 

5292 

5337 

5382 

967 

5426 

5471 

55i6 

556i 

56o6 

565i 

5696 

574i 

5786 

583o 

968 

5875 

5920 

5965 

6010 

6o55 

6100 

6i44 

6189 

6234 

6279 

969 

6324 

636g 

64i3 

6458 

65o3 

6548 

6593 

6637 

6682 

6727 

970 

6772 

6817 

6861 

6906 

6951 

6996 

7040 

7085 

7i3o 

7i75 

971 

7219 

7264 

73o9 

7353 

7398 

7443 

7488 

7532 

7577 

7622 

972 

7666 

7711 

7756 

7800 

7845 

7890 

7934 

7979 

8024 

8068 

973 

8n3 

8i57 

8202 

8247 

8291 

8336 

838i 

8425 

847o 

85i4 

974 

8559 

86o4 

8648 

8693 

8737 

8782 

8826 

8871 

8916 

8960 

975 

9005 

9049 

9094 

9i38 

9183 

9227 

9272 

93x6 

9361 

94o5 

976 

945o 

9494 

9539 

9583 

9628 

9672 

9717 

9761 

9806 

985o 

44 

977 

9895 

9939 

9983 

..28 

..72 

.117 

.161 

.206 

.25o 

.294 

978 

990339 

o383 

0428 

0472 

o5i6 

o56i 

o6o5 

o65o 

0694 

0738 

979 

0783 

0827 

0871 

0916 

0960 

ioo4 

1049 

1093 

1137 

1182 

980 

1226 

1270 

i3i5 

1359 

i4o3 

1 448 

1492 

i536 

i58o 

1625 

981 

1669 

1713 

i758 

1802 

1 846 

1800 

1935 

1979 

2023 

2067 

982 

211 1 

2i56 

2200 

2244 

2288 

2333 

2377 

2421 

2465 

2509 

983 

2554 

2598 

2642 

2686 

2730 

2774 

2819 

2863 

2907 

2951 

984 

2995 

3o39 

3o83 

3l27 

3l72 

32i6 

3260 

33o4 

3348 

3392 

985 

3436 

348o 

3524 

3568 

36i3 

3657 

3701 

3745 

3789 

3833 

986 

3877 

3921 

3965 

4009 

4o53 

4097 

4i4i 

4i85 

4229 

4273 

987 

43i7 

436i 

44o5 

444g 

4493 

4537 

458i 

4625 

4669 

47i3 

988 

4757 

4«oi 

4845 

4889 

4933 

4977 

5o2i 

5o65 

5io8 

5i52 

989 

5196 

524o 

5284 

5328 

5372 

54i6 

5460 

55o4 

5547 

5591 

990 

5635 

5679 

5723 

5767 

58n 

5854 

5898 

5g42 

5986 

6o3o 

991 

6074 

61 17 

6161 

6205 

6249 

6293 

6337 

638o 

6424 

6468 

992 

65i2 

6555 

6599 

6643 

6687 

6731 

6774 

6818 

6862 

6906 

993 

6949 

6993 

7o37 

7080 

7124 

7168 

7212 

7255 

7299 

7343 

994 

7386 

743o 

7474 

75i7 

756i 

7605 

7648 

7692 

7736 

7779 

995 

7823 

7867 

7910 

7954 

7998 

8o4i 

8o85 

8129 

8172 

8216 

996 

8259 

83o3 

8347 

8390 

8434 

8477 

852i 

8564 

8608 

8652 

'    997 

8695 

8739 

8782 

8826 

8869 

8913 

8956 

9000 

9043 

9087 

99S 

9i3i 

9174 

9218 

9261 

93o5 

9348 

9392 

9435 

9479 

9522 

999 

9565 

9609 

9652 

9696 

9739 

9783 

9826 

9870 

99i3 

9957 

43 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

.  f 

46  a  f  5 

9 

i4 

18 

23 

28 

32 

37 

4i 

1 

45  J3J   5 

9 

14 

18 

23 

27 

32 

36 

4i 

g 

44  M   4 

9 

i3 

18 

22 

26 

3i 

35 

4o 

Ql 

43  *  | 

4 

9 

i3 

17 

22 

26 

3o 

34 

39 

1 

TABLE 


OF 


LOGARITHMIC  SINES  AND  TANGENTS 


FOR   EVERY 


TEN  SECONDS  OF  THE  QUADRANT. 


L12 

LoGARI 

TIIMiC 

S  I  N  EH. 

Min. 

Sine  of  C 

)  Degree. 

P.  Pan 

tol". 

0" 

10" 

20" 

30'' 

40" 

50" 

o 

Inf.  Neg. 

5.685575 

5.986605 

6.162696 

6.287635 

6.384545 

59 

1 

6.463726 

6.530673 

6.588665 

639817 

685575 

726968 

58 

2 

764756 

799518 

83i7o3 

861666 

889695 

916024 

57  1 

3 

940847 

964328 

986605 

7.007794 

7.027997 

7.o473o3 

56 

4 

7.065786 

7.o835i5 

7.100548 

1 16939 

132733 

147973 

55 

5 

162696 

176936 

190725 

204089 

217054 

229643 

54 

6 

241877 

253776 

265358 

276639 

287635 

298358 

53 

7 

308824 

319043 

329027 

338787 

348332 

357672 

52 

8 

3668i6 

37577i 

384544 

393145 

401578 

409850 

5i 

9 

417968 

425937 

433762 

44i449 

449002 

456426 

5o 

:o 

463726 

470904 

477966 

4849i5 

491754 

498488 

49 

689.4 

ii 

5o5n8 

5 1 1649 

5i8o83 

524423 

530672 

536832 

48 

629.4 

12 

542906 

548897 

5548o6 

56o635 

566387 

572065 

47 

579.i 

i3 

577668 

5832oi 

588664 

594059 

599388 

6o4652 

46 

536.2 

i4 

609853 

614993 

620072 

625093 

63oo56 

634964 

45 

499.2 

i5 

639816 

6446 1 5 

649361 

654o56 

658701 

663297 

44 

467.0 

16 

667845 

672345 

676799 

681208 

685573 

689895 

43 

438.7 

17 

694173 

698410 

702606 

706762 

710879 

714957 

42 

4i3.6 

18 

718997 

722999 

726965 

730896 

734791 

73865i 

4i 

391.3 

J9 

742478 

746270 

75oo3i 

753758 

757455 

761119 

4o 

371.2 

20 

7647.54 

768358 

771932 

775477 

778994 

782482 

39 

353.1 

21 

785943 

789376 

792782 

796162 

79g5i5 

'  802843 

38 

336.7 

2  2 

806146 

809423 

812677 

815906 

819111 

822292 

3? 

321  .7 

23 

82545i 

828586 

831700 

834791 

837860 

840907 

36 

3o8.o 

24 

843934 

846939 

849924 

852889 

855833 

858757 

35 

295.4 

25 

861662 

864548 

8674i5 

870262 

873092 

875902 

34 

283.8 

26 

878695 

881470 

884228 

886968 

889690 

892396 

33 

273.1 

27 

895085 

897758 

900414 

9o3o54 

905678 

908287 

32 

263.2 

28 

910879 

913457 

916019 

9i8566 

921098 

923616 

3i 

254.0 

29 

926119 

928608 

931082 

933543 

935989 

938422 

3o 

245.4 

3o 

940842 

943248 

94564i 

948020 

950387 

952741 

29 

237.5 

3i 

955082 

957411 

959727 

962031 

964322 

966602 

28 

229.8 

32 

968870 

971126 

973370 

9756o3 

977824 

980034 

27 

222.7 

33 

982233 

984421 

986598 

988764 

990919 

993064 

26 

216. 1 

34 

995198 

997322 

999435 

8.ooi538 

3  .oo363i 

8.005714 

25 

209.8  ; 

35 

8.007787 

8.009850 

8.011903 

013947 

015981 

oi8oo5 

24 

203.0 

36 

020021 

022027 

024023 

02601 1 

027989 

029959 

23 

198.3 

37 

031919 

033871 

o358i4 

037749 

039675 

041592 

22 

iq3.o 

38 

o435oi 

o454oi 

047294 

049178 

o5io54 

052922 

21 

188.0 

39 

054781 

o56633 

o58477 

o6o3i4 

062142 

063963 

20 

i83.s 

4o 

065776 

067582 

069380 

071171 

072955 

074731 

*9 

178.7 

4i 

076500 

078261 

080016 

081764 

o835o4 

o85238 

18 

174.4 

42 

086965 

088684 

090398 

092104 

093804 

095497 

17 

170.3 

43 

097183 

098863 

100537 

102204 

io3864 

io55i9 

16 

166.4 

44 

107167 

108809 

no444 

1 12074 

113697 

u53i5 

i5 

162.6 

45 

116926 

n8532 

I20l3l 

121725 

i233i3 

124895 

i4 

159. 1 

46 

126471 

128042 

129607 

i3ii66 

132720 

134268 

i3 

i55.6 

47 

i353io 

i37348 

138879 

i4o4o6 

141927 

143443 

12 

i52.4 

43 

144953 

146458 

147959 

149453 

150943 

152428 

11 

149.2 

49 

:53qo7 

i55382 

i56852 

i583i6 

159776 

i6i23i 

10 

146.2 

5o 

162681 

164126 

165566 

167002 

168433 

169859 

9 

i43.3 

5i 

171280 

172697 

174109 

175517 

176920 

178319 

8 

i4o.5 

52 

179713 

i8iio3 

182488 

183869 

185245 

186617 

7 

i37.9 

53 

i87985 

189348 

190707 

192062 

ig34i3 

194760 

6 

i35.3 

54 

196102 

197440 

198774 

200104 

20i43o 

202752 

5 

i32.8 

55 

204070 

205384 

206694 

208000 

209302 

210601 

4 

i3o.4 

•56 

211895 

2-3i85 

214472 

215755 

217034 

218309 

3 

128. 1 

57 

219581 

220849 

222II3 

223374 

22463l 

225884 

2 

125.9 

58 

227134 

228380 

229622 

23o86i 

232096 

233328 

1 

123.7 

59 

234557 

235782 

237003 

238221 

239436 

240647 

0 
Min. 

121. 6 

. 

80" 

50" 

40" 

30" 

20" 

10" 

1 

( 

Ho-sine  of  § 

9  Degrees 

Logarithmic    Tasoents. 


23 


Min. 

Tangent  of  0  Degree 

f    V 

10" 

20" 

30" 

40'' 

50" 

o 

Inf.  Neg. 

5.685575 

5.9866o5 

6. 162696 

6.287635 

6,384545 

I 

6.463726 

6.53o673 

6.588665 

6398I7 

685575 

726968 

2 

764756 

799518 

83i7o3 

861666 

889695 

916024 

3 

940847 

964329 

986605 

7.007794 

7  027998 

7.o473o3 

4 

7.065786 

7.o835i5 

7. ioo548 

1 16939 

132733 

147973 

5 

162696 

176937 

190725 

204089 

217054 

229643 

6 

241878 

253777 

265359 

276640 

287635 

298359 

7 

3o8825 

319044 

329028 

338788 

348333 

357673 

8 

366817 

375772 

384546 

3g3i46 

401579 

409852 

9 

417970 

425939 

433764 

44i45i 

449004 

456428  1 

L 

lO 

463727 

470906 

477968 

484917 

491756 

498490 

ii 

5o5i2o 

5ii65i 

5i8o85 

524426 

530675 

536835 

72 

542909 

548900 

5548o8 

56o638 

566390 

572068 

13 

577672 

5832o4 

588667 

594062 

599391 

6o4655 

i4 

609857 

614996 

620076 

625097 

63oo6o 

634968 

t5 

639820 

644619 

649366 

654o6i 

658706 

6633o2 

16 

667849 

672350 

676S04 

68i2i3 

685578 

689900 

<7 

694179 

698416 

702612 

706768 

7io885 

714963 

18 

719003 

723oo5 

726972 

730902 

734797 

738658 

*9 

742484 

746277 

750037 

753765 

757462 

761127 

ZO 

764761 

768365 

771940 

775485 

779002 

782490 

21 

78595i 

789384 

792790 

796170 

799524 

802852 

22 

8o6i55 

809433 

812686 

815915 

819120 

822302 

23 

825460 

828596 

831710 

8348oi 

837870 

840918 

24 

843944 

846950 

849935 

852900 

855844 

858769 

25 

861674 

86456o 

867426 

870274 

873104 

875915 

26 

878708 

88i483 

884240 

886981 

889704 

892410 

27 

895099 

897772 

900428 

903068 

905692 

908301 

28 

910894 

913471 

916034 

9i858i 

921113 

92363i 

29 

926134 

928623 

931098 

933559 

936006 

938439 

3o 

94o858 

943265 

945658 

948037 

95o4o4 

952758 

3i 

955ioo 

957428 

959745 

962049 

964341 

966621 

32 

968880. 

97"45 

973389 

975622 

977844 

980054 

33 

982253 

98444i 

986618 

988785 

990940 

993o85 

34 

995219 

997343 

999457 

8.ooi56o 

8.oo3653 

3.oo5736 

-35 

8  007809 

8.009872 

8.01 1926 

013970 

016604 

018029 

36 

020044 

022o5l 

024048 

026o35 

028014 

029984 

37 

031945 

033897 

o3584o 

037775 

039701 

041618 

38 

043527 

045428 

047321 

049205 

o5io8i 

052949 

39 

054809 

o56662 

o585o6 

060342 

0621 71 

063992 

4o 

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43 

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090431 

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097217 

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102239 

103900 

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45 

116963 

118569 

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121763 

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46 

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128081 

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138921 

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190760 

192115 

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54 

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55 

204126 

20 5440 

206750 

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227195 

228442 

229685 

230924 

232160 

233392 

J.9. 

234621 

235846 

237068 

238286- 

239502 

240713 

60" 

50" 

40" 

30" 

20" 

10" 

Cc 

-tangent  0 

"  89  Degre 

es. 

,  . 

p.  r«it 

tol". 

59 

58 

1 

57 

56 

• 

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54 

53 

52 

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7 

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6 

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5 

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4 

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3 

128  1 

2 

125.9 

1 

123.8 

0 

121 .7 

Min. 



24 

LOGAI.  fTHMIC 

b'lNES. 

i 

|  MVo 

1 

Sine  of  ] 

Degree. 

F.  Part 
tol" 

119. 6 

V 

10" 

20" 

30" 

40" 

50-'' 

O 

8.24i855 

8.243o6o 

8.244261 

8.245459 

8.246654 

8.247845 

59 

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249033 

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252578 

253753 

254925 

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256094 

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286521 

287608 

288692 

53 

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289773 

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296207 

297270 

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299388 

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306721 

307759 

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8.308794 

8.309827 

8.3io857 

8.3n885 

8.312910 

8.3l3933 

49 

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316987 

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319012 

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321027 

322o3l 

323o33 

324o32 

325029 

326024 

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99.8 

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327016 

328007 

328995 

329980 

330964 

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98.5 

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332924 

333901 

334876 

335848 

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97.1 

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338753 

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340679 

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342596 

343551 

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345456 

3464o5 

347352 

348297 

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43 

94.6 

17 

35oi8i 

351119 

352o56 

352991 

353924 

354855 

42 

93.4 

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355783 

356710 

357635 

358558 

359479 

360398 

4i 

92.2 

J9 

36i3i5 

362a3o 

363i43 

364o55 

364964 

36587i 

4o 

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20 

8.366777 

8.36768i 

8.368582 

8.369482 

8.370380 

8.371277 

39 

89.9 

21 

372171 

373063 

373954 

374843 

375730 

3766i5 

38 

88.8 

22 

377499 

378380 

379260 

38oi38 

38ioi5 

381889 

37 

87.7 

23 

382762 

383633 

3845o2 

385370 

386236 

387100 

36 

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387962 

388823 

389682 

390539 

391395 

392249 

35 

85.6 

25 

393101 

393951 

394800 

395647 

396493 

397337 

34 

84-6 

26 

398179 

399020 

399859 

400696 

4oi532 

4o2366 

33 

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27 

403199 

4o4o3o 

404859 

405687 

4o65i4 

407338 

32 

82,7 

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408983 

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410621 

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3i 

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29 

4i3o68 

4i388o 

414691 

4i55oo 

4i63o8 

417114 

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80.8 

3o 

8.417919 

8.418722 

8.419524 

8.42o325 

8.421123 

8.421921 

29 

80.0 

3i 

422717 

4235n 

4243o4 

425096 

425886 

426675 

28 

79.1 

32 

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428248 

429032 

429815 

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78.2 

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433710 

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439868 

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25 

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24 

75.  € 

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22 

74.2 

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458570 

21 

73.5 

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459301 

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460761 

461489 

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20 

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8.463665 

8.464388 

8.465no 

8.46583o 

8.46655o 

8.467268 

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468701 

469416 

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71.3 

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472971 

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477901 

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16 

69. 9< 

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48i388 

482083 

482776 

483467 

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69.2 

45 

484848 

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68.6 

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488963 

489645 

490326 

491006 

491685 

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493715 

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495736 

496408 

12 

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48 

497078 

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498416 

499084 

499730 

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11 

66.7 

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5oio8o 

5oi743 

5o24o5 

5o3o67 

503727 

5o4386 

10 

66.1 

5o 

8.5o5o45 

8.505702 

8.5o6358 

8.507014 

8.507668 

8.5o832i 

9 

65  5 

5i 

508974 

509625 

510275 

510925 

5n573 

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64.9 

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5i35i3 

5i4i57 

5i48oi 

5 1 5444 

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5i8oo5 

5i8643 

519280 

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6 

63.7 

54 

52o55i 

521186 

521819 

52245i 

523o83 

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5 

63.2 

55 

524343 

524972 

525599 

526226 

526852 

527477 

4 

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528102 

528725 

529347 

529969 

530590 

531209 

3 

62.1 

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531828 

532446 

533o63 

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536i36 

536747 

537358 

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1 

61. 1 

59 

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539i86 

539794 

54o4oi 

541007 

541612 

542216 

0 

6o.5 

60" 

50" 

40" 

30" 

20" 

10" 

Min. 

( 

^o-sine  of  8 

8  Degrees 

Logarithmic    Tangents. 


25 


Min. 
o 

1 

Tangent  < 

>f  1  Degree. 

P.  Pait 
tol". 

1  ■  o» 

10" 

20" 

30" 

40" 

50" 

8.241921 

8.243l26 

8.244328 

8.245526 

8.246721 

8.247913 

59 

119. 7 

I 

249102 

250287 

251469 

252648 

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58 

117. 7 

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272213 

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275576 

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112. 2 

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278913 

280020 

281124 

282225 

54 

no. 5 

6 

283323 

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286602 

287689 

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53 

108.9 

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289806 

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52 

107.2 

6 

296292 

297355 

298416 

299474 

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105.7 

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302634 

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304727 

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307849 

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104.2 

IO 

8.3o8884 

8.309917 

8.310948 

8.311976 

8.3i3oo2 

8.3i4o25 

49 

102.7 

ii 

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3i6o65 

3 1 708 1 

318095 

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320ii5 

48 

101 .3 

12 

32II22 

322127 

323129 

324129 

325i26 

326121 

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99.8 

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327114 

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329093 

33oo8o 

33io64 

332045 

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98.5 

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333025 

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336921 

337890 

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338856 

339821 

340783 

34i743 

342701 

343657 

44 

95.9 

16 

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345562 

3465i2 

347459 

3484o5 

349348 

43 

94.6 

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350289 

351229 

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353ioi 

354o35 

354966 

42 

93.4 

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356823 

357748 

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92.2 

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362345 

363259 

364171 

365o8i 

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91. 1 

20 

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8.367799 

8.368701 

8.369601 

8.37o5oo 

8.371397 

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374076 

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8.418068 

8.418872 

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60" 

50" 

40" 

30" 

20" 

10" 

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Min. 

2G 


Logarithmic    Sines. 


i 
9 

Sine  of  2  Degrees. 

3 

Sine  of  3  Degrees. 

... 
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30' 

40" 

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40" 

30''  j  20" 

10" 

c 

60*    |  50"  |  40"  j  30"  t  20"   10* 

7! 

*  ! 

Co-sine  of  83  .Degrees. 

8 

Co-sine  of  82  Degrees. 

,   <  1"  2"  3''  4"  5"  6"  7"     8"  9" 
'-*  \   18  37  55  74  92  111  12.9  148  166 

r.i 

^     t    J//  O//   3//   4//   5//   g//   7//    g7   Q» 

&    }   16  32  48  C4  80  96  112  128  144 

] 

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• 

31 

1 

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i 

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0 
A 

60" 

50" 

40"  |  30"  1  20"  |  50" 

60" 

50"  1  40" 

30" 

20"  1  10" 

Co-tangent  of  83  Degrees. 

Co-tangent  of  82  Degrees. 

P.  1 

,   J  1"  2"  3"  4"  5"  6"  7"     8"  9"   {!  p 
}  19  37  56  75  94  112  131  150  16S  l  ' 

p  i  1"  2"  3"  4"  5"  6" 
l'in\   16  33  49  65  81  98 

114 

87 
130 

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32 

L 

ogahithmic  Sines. 

17 

Sine  of  8  Degrees. 

t 

Sine  of  9  Degrees. 

o 

0" 

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30" 

40" 

50" 

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20" 

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Co-sine  of  72  Degrees. 

P. 



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Co-tangent  of  72  Degrees. 

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Co-sine  of  70  Degrees. 

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Co- tangent  of  71  Degrees. 

Co-tangent  of  70  Degrees. 

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9.588890 

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9090  9140 

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9.6o6465 

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6608 

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9190 

9240  9290  9340 

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7417 

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9029 

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60" 

50"  |  40"  1  30" 

20"  |  10" 

3 

| 

60" 

50" 

40"  |  30" 

20" 

10" 

i 

5S 

Co-sine  of  67  Degrees. 

Co-sine  of  66  Degrees. 

P. 

p   <  1"  2"  3"  4"  5"  G"  7"    8"    9" 
raTl\   5  10  15  20  25  31  36  41  46 

P. 

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8" 
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9"  ' 

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Logarithmic    Tangent h. 


47 


Tangent  of  22  Degrees. 


10"   20"  I  30"   40"  I  50" 


Tangent  of  23  Decrees. 


10"   20" 


40"   50" 


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9312 
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1 180  ia4o 
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1601 
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2621  268l 

2981  3o4i 

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256i|2620;2679  2738 


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3858  39i7 
4212  4271 


574i;58oo'5858 
60936152  621 1 
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7149 
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9.63i355 
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7149  7207 


7495 
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9222(9280 

956719625 

9912I9969 

0257  o3i4 

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0945  1002 

1289  1 346 

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1976  2o34 

23202377 

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3oo6i3o63 
3349  34o6 
3691  3749 
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4376  4433 

47i84775 
5o6o  5i  17 
54o2  5459 
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6369'6426  6483 
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7o5i  7108  7165 
7392  74497506 
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8o73;8i3o8iS6 
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5o 

58 

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56 
55 

54 
53 

52 

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5o 

49 

48 

47 
46 
45 
44 
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39 
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35 
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50"  40"     ;«y  I  20" 


Co-tangent  of  G7  Degrees. 


/  til      o"   •!» 


30 


'JO 


18 

L 

0  G  A  R  I  T  I!  M  1 

D  SlNF 

S. 

o 

Sine  of  24  Degrees. 

2 

Sine  of  25  Degrees. 

0" 

10" 

20"  |  30" 

40"  |  50" 

0" 

10"  1  20"  j  30" 

40'' 

50" 

9. 609313 

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9408^455 

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9.633984 

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9i55 

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9.623229 

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9.639242 

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9373  9416 

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53 

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54 

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55 

4591 

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0674  0718 

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56 

4863 

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5i35  5i8o 

5225 

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2 

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1194  12  37 

1280 

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5542!5587 

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59 

56775722 

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i5S3|  1 626  1669 

1712I1756 

1799 

0  1 

60"    |  50" 

40" 

30"  j  20" 

10" 

3 

f>0"    |  50"  |  40"  |  30"  |  20"  I  10" 

40  j 

Co- sine  of  G5  Degrees. 

Co-sine  of  64  Degrees. 

P. 

1 

v       i  1"  2"  3"  4"  5"  6"  7"    8"  9" 
1  a  \   5   9  14  18  23  28  32  37  42 

P. 

C  1"  0"  3"  4"  5"  6"    1"    8" 
ldrt}  4   9  13  18  22  2C  31  35 

Logarithmic    Tangents. 


49 


0" 


Tangent  of  24  Degrees. 
r  I  30* 


40"       50" 


Tangent  of  25  Degrees. 


10"   90" 


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Co-tangent  of  G5  Degrees. 


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"  W        lo"  W 


Co-tangenl  of  6-1  Degree* 


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ci 

60"    |  50"  |  40"  1  30" 

20"  |  10" 

d 

Co-sine  of  63  Degrees. 

Co-sine  of  62  Degrees. 

P. 

Fart?  \ 
I    4 

2«  3»  4'/ 
8  13  17 

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51 


Tangent  of  26  Decrees. 


Tangent  of  27  Degrees. 


30" 


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71 14 


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Co-tangcnt  of  02  Degrees.       j  3 

3"    4"    5"    6"    7"    8' 


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9' 
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s 

Sine  of  29  Degrees. 

0" 

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30" 

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50" 

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10" 

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60" 

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60"    |  50" 

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30"  |  20" 

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. 

Co-sine  of  6 1  Degrees. 

Co-sine  of  60  Degrees. 

1 

P. 

p  .(1"  2"  .3"  4"  5"  6"  7"  8"  9" 
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Logarithmic    Tangents. 


53 


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a 
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59 

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Part  j1; 


Co-tangent  of  53  Degrees. 

3"    4"    5"    6"    7"  IF" 
11    19    21    28    33    38 


I 


5G 

L 

0  O  . 

1  1:  I 

V  H  M  I  C  S  I  N  E  3. 

1  ri 

Sine  of  32  Degrees. 

Sine  of  33  Degrees. 

1 

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10" 

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40"  |  50" 

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50"  |  40" 

30"  j  20" 

10" 

3 

60"    |  50"  |  40" 

30"  |  20" 

10" 

a 

a 

Co-sine  of  57  Degrees. 

Co-sine  of  56  Degrees. 

r. 

p   <1"  2"  3"  4"  5"  6"  7"    8"    9" 
a  }    3  7  10  13  17  20  23  2G  30 

p  v      <1"  2"  3"  4"  5"  6"  7"    8"    9" 
1  -lAn\    3   6  10  13  1G  19  22  25  29 

LiOG  ARITH  M  I 

, 

Tangents 

. 

57 

!- 

Tangent  of  32  Degrees. 

I 

Tangent  of  33  Degrees. 

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0" 

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30" 

40" 

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1 

60"   |  50"  |  40" 

30"  |  20" 

10" 

3 

60"    |  50"  |  40" 

30"  |  20"  1  10"  j 

| 

Co-sine  of  53  Degrees. 

Co-sine  of  52  Degrees. 

3 

P.1 

<  1"  2"  3"  4"  5"    6"  7"    8"    9" 
a  I   3   6   9  11  14  17  20  23  26 

, ii 

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1.1  art£  3   5   g  n  H  16  19  22  25 

Logarithmic    Tangents. 


61 


Tangent  of  36  Degrees. 

V'  |T6"  I  20"  |  30"~|  40"~1  50" 


Tangent  of  37  Degrees. 


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Co-tangent  of  52  Degree. 

'J"  3"  4"  0"  6"  7'  8" 
9  13  17  52  CO  31  35 


02 

Logarithmic  Sines. 

a 

Sine  of  38  Degrees. 

1 
_a° 
8 

Sine  of  39  Degrees. 

r~ 

0"    |  10"  |  20"  |  30"   40"  |  50" 

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52 

8 

o632 

0659 

0686J0713 

0740 

0767  5i 

8 

9.800117 

oi43 

0169 

0195 

0220 

0246 

5i 

9 

o793 

0820 

0847 

0874 

0901 

0927  5o 

9 

0272 

0298 

o324 

o35o 

0376 

o4oi 

5o 

IO 

9.790954 

0981 

1008 

io34 

1 06 1 

1088 

49 

10 

9.800427 

o453 

0479 

o5o5 

o53i 

o556 

49 

ii 

1 1 15 

1142 

1168 

1 195 

1222 

1249 

48 

1 1 

o582 

0608 

0634 

0660 

0686 

071 1 

48 

12 

1275 

i3o2  1329 

i356 

i382 

1409 

47 

12 

0737 

0763 

0789 

o8i5 

o84o 

0866 

47 

i3 

i436 

1 463  1489- 

i5i6 

1 543 

1570 

46 

i3 

0892 

0918 

0944 

0969 

0995 

1 02 1 

46 

r4 

1596 

i623i65o 

1676 

1703 

1730 

45 

i4 

1047 

1073 

1098 

1 1 24 

n5o 

1 1 76 

45 

i5 

i757 

1783  1810 

i837 

i863 

1890 

44 

i5 

1201 

1227 

1253 

1279 

i3o5 

i33o 

44 

iG 

1917 

1943 

1970 

1997 

2024 

2o5o 

43 

16 

i356 

i382 

i4o8 

i433 

1459 

i485 

43 

*7 

2077 

2I04 

2i3o 

2157 

2184 

2210 

42 

17 

i5ii 

i536 

i562 

i588 

i6i3 

1639 

42 

18 

2237 

2264  2290 

2317 

2344 

2370 

4i 

18 

i665 

1691 

1716 

1742 

1768 

1794 

4i 

J9 

2397 

2423 245o 

2477 

25o3 

253o 

4o 

*9 

1819 

i845 

1871 

1896 

1922 

i948 

4o 

20 

9.792557 

2583  2610 

2636 

2663 

2690 

39 

20 

9.801973 

1999 

2025 

2o5l 

2076 

2102 

39 

21 

2716 

2743  2770 

2796 

2823 

2849 

38 

21 

2128 

2i53 

2179 

22o5 

2230 

225638 

22 

2876 

2903  2929 

2956 

2982 

3009 

3? 

22 

2282 

2307 

2333 

2359 

2384 

2410  37 

23 

3o35 

3062  3089 

3i  1 5 

3l42 

3i68 

36 

23 

2436 

2461 

2487 

25l2 

2538 

2564136 

24 

3195 

3222  3248'3275 

33oi 

3328 

35 

24 

25S9 

26i5 

2641 

2666 

2692 

2718 

35 

a  5 

3354 

3381:34073434 

346o 

3487 

34 

25 

2743 

2769 

2794 

2820 

2846 

2871 

34 

26 

35i4 

3540  3567 

3593 

3620 

3646 

33 

26 

2897 

2922 

2948 

2974 

2999 

3o25 

33 

27 

3673 

3699  3726 

3752 

3779 

38o5 

32 

27 

3o5o 

3o76 

3l02 

3l27 

3i53 

3i78 

32 

28 

3832 

3858  3885 

3911 

3938 

3964 

3i 

28 

3204 

3229 

3255 

328l 

33o6 

3332 

3i 

29 

399i 

4oi7  4o44 

4070 

4097 

4123 

3o 

29 

3357 

3383 

34o8 

3434 

3459 

3485 

3o 

3o 

9.794i5o 

4176  42o3 

4229 

4255 

4282 

29 

3o 

9.8o35n 

3536 

3562 

3587 

36i3  3638 

29 

3i 

43o8 

4335  4361 

4388 

44i4 

444 1 

28 

3 1 

3664 

3689 

37i5 

3740 

3766 

379i 

28 

32 

4467 

4493  4520 

4546 

4573 

4599 

27 

j2 

38i7 

3842 

3868 

3893 

3919I3944 

27 

33 

4626 

4652!4678 

47o5 

473i 

4758 

26 

33 

3970 

3995 

4o2I 

4o46 

4072  U097 

26 

34 

4784 

48io4837 

4863 

4890  4916 

25 

34 

4l23 

4i48  4174 

4199 

42a5  4s5o 

25 

35 

4942 

4969  4995|5o22 
5127  5i54  5i8o 

5o48  5o74 

24 

35 

4276 

43oi 

4327 

4352  4377!44o3 

24 

36 

5ioi 

52065233 

23 

36 

4428 

4454 

4479 

45o5 

453o{4556 

23 

'^7 

5259 

5285  53i2 

5338 

5364 5391 

22 

37 

458i 

4607 

4632 

4657 

46834708 

22 

38 

54i7 

5443  5470 

5496 

5522  5549 

21 

38 

4734 

4759 

4784 

4810 

4835486i 

21 

39 

5575 

56oi  5628 

5654 

568o  5707 

20 

39 

4886 

4912 

4937 

4962 

4988  5oi3 

20 

4o 

9.795733 

5759  5786 

58i2 

58385865 

*9 

4o 

9.8o5o3g 

5o64 

5089 

5n5 

5i4o 

5 1 65 

l9 

4i 

589I 

5917  5943 

597o 

5996,6022 

l8 

4i 

5 19 1 

5216 

5242 

5267 

5292 

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l8 

42 

6o49  6075  6101  6127 

6i54:6i8o 

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42 

5343 

5368 

5394 

5419 

5444 

5470 

*7 

43 

6206 

6233  6259!6285  63u  6338 

16 

43 

5495 

5520 

5546 

557i 

5597 

5622 

16 

44 

6364 

639064166443:64696495 

i5 

44 

5647 

5673 

5698 

5723 

5748 

5774 

i5 

45 

652i 

6547  6574  6600,6626,6652 

i4 

45 

5799 

5824 

585o 

5875 

5900 

5926 

i4 

46 

6679 

6705673167576783:6810 

i3 

46 

5g5i 

5976 

6002 

6027 

6o52 

6077 

i3 

4? 

6836 

686268886914 

694^6967 
7098:7124 

12 

4? 

6io3 

6128 

6i53 

6179 

6204 

6229 

12 

48 

6993 

7019  7045J7072 

1 1 

48 

6254 

6280 

63o5 

633o 

6355 

638i 

11 

49 

7i5o 

7176  7202  7229 

7255  7281 

10 

49 

64o6 

643 1 

6456 

6482 

6507 

6532 

IO 

5c 

9.797307 

7333  7359  7386 

7412  7438 

9 

5o 

9.806557 

6583 

6608 

6633 

6658  6684 

9 

5i 

7464 

7490  7516  7542 

7569 

7595 

8 

5i 

6709  6734 

6759 

6785 

68io6835 

8 

52 

7621 

7647  767317699 

7725 

775i 

7 

52 

686o6885 

691 1 

6936  6961  6986 

7 

53 

7777 

7804  7830  7856 

7882 

7908 

6 

53 

701 1 

7o37 

7062 

7087711217137 

6 

54 

7934 

7960798680128038  8o65 

5 

54 

7163 

7188 

72i3  7238  726357288 

5 

55 

8091 

8iz7'8i43  816918195:8221 

4 

55 

73i4  7339 

7364  7389  74147439 

4 

56 

8247 

8273  8299l8325  835il8377  3 

56 

7465  7490 

75157540,75657590 

3 

57 

84o3 

8429  8455  848i  85o8  8534  2 

57 

76i5  7641 

7666,7691  7716:7741 

2 

58 

856o  8586  86i2'8638j8664'869o 
8716  8742'8768!8794  8820:8846 

1 

58 

77667791 

78*6,7842  7867:7892 

1 

59 

0 

59 

791 7J7942  7967^992  8017  8042 

0 

60"    |  50"  |  40"  |  30"  |  20"  |  10" 

a" 

8 

60"    j  50"  |  40"  1  30"  |  20"  ,  10" 

a 

Co-sine  of  51  Degrees. 

Co-sine  of  50  Degrees. 

S 

V. 

„  .  S  1"  2"  3' 
IartJ3   5   8 

4" 
11 

5"  6"  7"    8"  9" 
13  16  19  21  24 

P. 

p  A  I"    2"  3"  4"  5"  6"  7"  8"  .0" 
lart\   3   5   8  10  13  15  18  20  S3 

Logarithm  ic    Tangents. 


63 


Tangent  of  38  Degrees. 
~0"   rid"  I  20"  I  30"  ~W' 


T" 


i 

2 

3] 
4 
5 
6 

7 
8 

9 
io  9 

ii 

12 

i3 

i4 
i5 

16 
'7 
18 

'9 

20  9. 

21 

22 

23 

24 

25 

26 

27 

289, 

29 

3o 
3i 

32 

33 

34 
35 
36 

37 
38 
39 

40  1 

4 1 
42 
43 
44 
45 
46 

47 

48 

49 

5o ' 
5i 

52 

53 
54 
55 
56 

57 
58 
59 


.S92810 
3070 
333i 
3591 
385i 
4ni 
4372 
4632 
489 


2853 
3n4 
3374 
3634 
3894 
4i55 
44i5 
4675 
4935 


5 1 52  5 195 


895412 
5672 
5932 
6192 
6452 
6712 
6971 
7231 
7491 
775i 

898010 
8270 
853o 
8789 


5455 
57i5 
5975 
6235 
6495 
6755 
70 1 5 
7275 
7534 
7794 
8o54 
83i3 
8573 
8832 
9049J9092  9135 
9395 


2897 
3i57 

34i7 
3678 
3938 

4198 
4458 
4718 

4979 
5239 

5499 
5759 
6019 

6278 
6538 
6798 
7o58 
73i8 
7578 
7837 
8097 
8357 
8616 
8876 


9654 


9308  935i 
9568:9611 
98279870J9914 
900087  oi3o  0173 
0389  o432 
06480692 


2940 
3200 
346i 
3721 
3981 
4241 
45o2 
4762 

5o22 
5282 
5542 

58o2 
6062 

6322 

6582 
6842 
7101 
736i 
7621 


2983 
3244 
35o4 
3764 
4o25 
4285 
4545 
48o5 
5o65 
5325 
5585 
5845 
6io5 
6365 
6625 
6885 
7i45 
74o4 
7664 


7881  7924 


8i4o 
84oo 
8659 
8919 
9178 


8i83 
8443 
8703 
8962 
9222 


o346 
.900605 


086410908,0951 


1 124 
i383 
1642 
1 90 1 
2160 
2420 
2679 
2938 
.903197 
3456 
37i4 
3973 

4232 

4491 
475o 

5oo8  5o52  5og5 
5267  53io5353 
5526556956i2 
.905785  58285871 
604360866129 
63o263456388 
656o66o3  6646 
6819  6862  6905 
7077I7120J7163 
,7336b379  74'J2 
759417637  7680 
7853  7896  7939 
8111  8i54  siv; 


I  I  67  I2IO 

14261469 

i685  1729* 

1944  1988 

2204|2247 

2463i25o6 
27222765 
2981  3o24 
324o3283 
3499^542 
3758]38oi 
4oi6  U060 
42754318 
45344577 
479314836 


94389481 
9697  9741 
9957  .... 
0216  0259 
0476  o5i9 
0735  0778 
0994  1037 
:253  1297 
1 5i  3  1 55G 
1772  i8i5 
2o3i  2074 
2290  2333 
2549  2592 
28082851 
3067  3i  10 


3326 
3585 
3844 
4io3 
4362 
4620 

4879 
5 1 38 


3369 
3628 
3887 
4i46 
44o5 
4663 
4922 
5i8i 


5397  r)44o 
5655  5698 
5914  5957 
6172  6216 


643i 
6690 


6474 
6733 
69481699 1 
7207  7250 
7465|75o8 
7723|7766 
798218025 
82408283 


<W"_  I  ar<  |  40"  |  :to»  a 
Co-tangent  of  51  Decrees 


3027 
3287 
354? 
38o8 
4o68 
4328 
4588 
4848 
5 1 09 
5369 
5629 
5889 
6149 
64o8 
6668 
6928 
7188 
7448 

7707 
7967 

8227 
8486 
8746 
9005 
9265 
9524 
9784 
..43 
o3o3 
o562 
0821 
1081 
1 34o 
i599 
i858 
2117 
2376 
2635 
2894 
3i53 
34i2 
3671 
3930 
4i89 
4448 
4707 
4965 

5224 

5483 
574i 
6000 

6259 

65i7 
6776 
7034 
729') 
755i 
7809 
8068 

~10" 


Tangent  of  39  Degrees. 


v 


I  10"  I  20"  I  30"  I  40"  I  50" 


I 

2 

3 

4 

5 
0 

7 
8 

9 

10  9 

11 

12 
i3 
i4 
i5 
16 

n 

IX 

'9 

2l) 


23 

2  4 
25 

26 
27 
28 
29 

3o 
3i 

32 

33 
34 
35 
36 

37 

38 
39 
4o 
4i 
42 
43 
44 
45 
46 

47| 
48 

49 

5o  9 

5i 

52! 

53 

54 

55 

56 

'7 
58 

59 


9o8369|84i2|8455 
86288671  8714 
888689298972 
9144  9187  9230 
9402  9445I9488 
966019703  9746 


9918J9961 
.910177  0220 


o435 

0693 

9 1 095 1 

1209 

1467 
1725 
1982 
2240 


27S6 
3oi4 
3271 
.913529 
3787 

•  4o44 

4302 

456o 
4817 

•  5075 
5332 
5590 


5 

0263 
o52i 

0779 

1037 
1295 
i553 
1810 
2068 
2326 
2584 
2842 
3 1 00 
3357 
36i5 
3873 
4i3o 
4388 
4645 
4903 
5i6i 
54i8 
5675 
5933 


TMnrt 


C  1"  2 
\    1   I 


0478 
0736 
0994 

1252 

i5io 

1768 

2025 

!283 

2541 

2799 

3o57 

33i4 

3572 

383o 

4o87 

4345 

46o3 

486o 

5n8 

5375 

5633 
58475890 
.916104  6147J6190 
636264o56448 
6619  6662:6705 
6877,6919  6962 
7i34  7177  7220 
7391  7434  7477 
7648  7691  7734 
7906794817991 
81638206.8248 
842o846385o6 
.918677J87208763 
8934:8977^9020 
9191I92349277 
9448^491,9534 
970597489791 
9962... 5.  48 

.920219  026.:  <)'!.>') 
0476  o5i9  o562 
0733:0776,0819 
0990  1033,1075 

.921247  1289  1 332 
1 5o3!  1 540, 1 589 
1760  i8o3  i846 
20172060  2io3 
2274,2316  2359 

253025732616 

27872830J2873 

3o44  3087  3129 
33oo  334:i  3386 
3557|36<>" 


8498 
8757 
9015 
9273 
953i 
9789 
48 
o3o6 
o564 
0822 
1080 


854i 
8800 
9o58 
9316 
9574 
9832 

91 
0349 
0607 
o8"65 

1123 


i338 i38i 
1596  i63g 
i853  1896 
211  i|2i54 

2369!24l2 

627  2670 
2885  2928 
3i43|3i85 
34oo  3443 
3658J37oi 
3916I3959 
4173  U216 
443i4474 
4688!473i 


4946 
52o3 
546i 
57i8 


4989 
5246 
55o4 
5761 


'9 
58 

57 

56 
55 
54 
5; 
5  a 
5i 
5,, 

48 

4? 

46 
45 
44 
43 

42 

4i 
4o 

39 

38 

37 
36 
35 

">4 
33 
3a 


8584 
8843 
9101 
9359 
9617 
875 
1 34 
0392 
o65o 
0908 
1166 
i424 
16S2 
i939 

21 97 

2455 
2713 
2971 

3228 
3486 
744 
4ooi 
4259 
45i7 
4774 
5o32 
5289 
5547 
58o4|3i 
6062  3o 
6319  29 
6576sS 
6791I6834  27 
7048  7091  26 
73o5734SJ25 
752o7563  7605  24 
77777820786323 
8034,8077,8120  22 
8291  8334'8377  21 
i8548  859i|8634l2o 
|88o5|S848'SS9 1(19 
9063  9105  9148  18 
93209362  94o5  17 
9577  96i9'9662ii6 
'9834.9876:9919  i5 
91  .i33.i76i4 
o348  o39o!o433  i3 
0604  0647  0690. 1 2 
0861  0904  0947  1 1 
1 1 18  1 161I1204  10 
1375  i4i8  i46i 
i63a  1C75  1717 
1889:1931  1 974 

2145  2l88  223l 

24"2  244j,2488| 
2659  2702  2744 
291  5  2958:3001 
3172  321 5  3258 
3429  3471  35 14 
3685  3728  3771 


5976,6019 

623316276 

6491  6533 

6748 

7oo5 

7262 


Co-tangent  of  50  Degrees. 


4" 
17 


:,"   <;"  7" 

2-2  26  30 


P.  Par,  I1,' 


3" 
13 


21 


2G 


7"    8'' 
30  31 


i 

>: 

!)" 

3:i 


64 

L 

iOGARITHMIC  S  1  N  E  S. 

i 

J 

Sine  of  40  Degrees. 

8 

Sine  of  41  Degrees. 

0"    1  10"  1  20"  |  30"  |  40" 

50" 

0"    1  10" 

20" 

30' 

40" 

50" 

o 

9,808067  8093  8118  8i43j8i68 

8193 

5o 

0 

9.816943I6967 

6991 

7016 

7040 

7064 

59 

I 

8218824382688293,8318 

8343 

58 

1 

7088 

7112 

7137 

7161 

7i85 

7209 

58 

2 

8368  8393,84i9  8444  8469 

8494 

57 

2 

7233 

7258 

7282 

73o6 

733o 

7354 

57 

3 

85i9 

8544|8569i8594  86i9 

8644 

56 

3 

7379 

74o3 

7427 

745i 

7475 

7499 

56 

4 

8669 

8694  8719  8744,8769 

8794 

55 

4 

7524 

7548 

7572 

7596 

7620 

7644 

55 

5 

8819 

88448869  8894 

8919 

8944 

54 

5 

7668 

7693 

7717 

7741 

7765 

7789 

54 

i  e 

8969 

899490199044 

90699094 

53 

6 

7813 

7837 

7862 

7886 

7910 

7934 

53 

1  7 

9119 

9144,91699194 

92I99244 

52 

7 

7958 

7982 

8006 

8o3o 

8o55 

8079 

52 

8 

9269 

92949319^344 

93699394 

5 1 

8 

8io3 

8127 

8i5i 

8i75 

8199 

8223 

5i 

9 

9419 

9444,9469.9494 

9519  9544 

5o 

9 

8247 

8272 

8296 

8320 

8344 

8368 

5o 

1  io 

9.809569 

9594961 919643 

9668  9693 

49 

10 

9.818392 

84i6 

844o 

8464 

8488 

85i2 

49 

i » 

9718 

97439768  9793 

98189843 

48 

11 

8536 

856o 

8584 

8609 

8633 

8657 

48 

12 

9868 

9893  99189943 

996719992 

47 

12 

8681 

87o5 

8729 

8753 

8777 

8801 

47 

i3 

9.810017 

0042  0067  0092 

0117  0142 

46 

i3 

8825 

8849 

8873 

8897 

8921 

8945 

46 

i4 

0167 

OI9I  02l6  024l 

0266  0291 

45 

i4 

8969 

8993 

9017 

9041 

9065 

9089 

45 

i5 

o3i6 

o34i  o366|o39o 

o4i5io44o 

44 

i5 

9113 

9i37 

9161 

9i85 

9209 

9233 

44 

16 

o465 

0490  o5i5  o54o 

o564io589 

43 

16 

9257 

9281 

93o5 

9329 

9353 

9377 

43 

17 

o6i4 

0639066410689 

0713  0738 

42 

J7 

9401 

9425 

9449 

9473 

9497 

9521 

42 

18 

o763 

o788o8i3,o838 

0862  0887 

4i 

18 

9545 

9569 

9593 

9617 

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9689 

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20 

9.811061 

1086,111011135 

1 1 60 

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39 

20 

9.819832 

9856 

9880 

9904 

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21 

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1 309 

i334 

38 

21 

9976 

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22 

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2347,2372 

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1026 

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1074 

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2  9 

2396 

2421  2446  2470 

2495  2520 
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3o 

29 

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9.812544 

2569  2594  26l8 

29 

3o 

9.821265 

1288 

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i336 

i36o 

1 384 

29 

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2692 

2717  2742,2766 

279I  28l5 

28 

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28 

32 

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2865  28892914 

2939  2963 

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22 

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9.822688 

2712 

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4240 

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18 

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2878 

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42 

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9 

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7 

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6 

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6094  6 u 8; 6 142,6 1 67  6 1 91 

5 

54 

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4738 

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5 

55 

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4 

55 

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4 

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3 

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3 

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2 

57 

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5 1 36 

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5i83 

5207 

2 

58 

6652  6676  6701  6725,6749  6773 

1 

58 

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5254 

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1 

59 

6798|6822l6846  6870  6894  6919 

0 

59 

5371 

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0 

I 

60"    |  50"  j  40"  J  30"  j  20"  1  10" 

3 

60" 

50"  |  40" 

30" 

20" 

10' 

a 

3 

Co-sine  of  49  Degrees. 

Co-sine  of  48  Degiees. 

;-■ 

p  .<  1"  2"  3"  4"  5"  6"  7"  8"  9" 
1       I   2   5   7  10  12  15  17  20  22 

P. 

C  1"  2"  3"  4"  5"  6"  7"    8"  9" 
lart}  2  5   7  10  12  14  17  19  21 

Logarithmic  Tangents. 


65 


Tangent  of  40  Degrees. 


09 

1 

2 

3 

4 

5 

6 

7 

8 

9 
109 

11 
12 
i3 
i4 
i5 
iC 

17 
18 

*9 

20  9 

21 

22 

23 

24 

25  ( 

26 
27 

28 

29 

3o( 
3i 

32 

33 
34 
35 
36 

37 
38 
39 
4o  < 

4i 
4a 
43 

44 
45 
46 

hi 

48 

49 

5o  1 
5-1 

52 

53 
54 
55 
56 

57 
58 
5q 


.923814 

4070 

4327 

4583 

484o 

5096 

5352 

5609 

5865j59o8 

6i22|6i64 
.92637616421 


10"   20"   30"   40"   50" 


3856 
4n3 
4369 
4626 
4882 
5i39 
53g5 
5652 


3899 
4i56 
44i2 
4669 
492S 
5i8i 
5438 
56g4 
5951 
6207 
6463 


6634  6677I6720 


6890,6933 


7147 
74o3 
7659 
79i5 
8171 
8427 
8684 
.928940 
9196 
_  9452 
9708 
9964 


7189 
7446 
7702 


697C 
7232 


3942 

4198 
4455 
4711 
4968 

5224 

5481 

5737 
5993 
625o 
65o6 
6762 
7019 
7275 


7488  753 
7744  — 


79588001 
82148257 
8470  85i3 
8726  8769 
898219025 
9238I9281 
9494|9537 

975o|9793 
.6|. .49 


.930220  0262 ,o3o5 
o475  o5i8  o56i 


3985  U027 


424i 
4498 
4754 
5oi  1 
5267 
5523 
5780 
6o36 
6292 
6549 


4284 
454o 

4797 
5o53 
53io 
5566 

5822 

6079 
6335 
6591 


7787 

8o43 

8299 

8555 

8812 

9068 

9324 

g58o 

9836 

..92 

o348 

o6o3 

0731  0774|o8i7|o859 

0987  1030J1073  11 15 

1243  1286J1328  1371 

.931499  i542ji584  1627 

1755  1797  1 84o  1 883 

2010  2o53  2096  2i38 

226612309  235 1  2394 

2522  2565 : 2607  265o 

2778:28201286312906 

3o33|3o76  3ii9|3i6i 

3289  3332  33743417. 

3545!3587363o3672 

38oo'3843  3885  3928 

.934o56!4o98  4i4i  4i84 

43 1 1 14354  4397  4439 

4567'46io'4652  4695 

4822U865I49084950 

5o78i5i2i5i63  52061 

5333|5376!54i9l546i 

5589!5632|5674  57i7 

5844  5887  593o!5972 

61006142  61856227 

6355,6398  6440  6483 

.936G1  il6G53|6696|6738 

68G6  6908  6951 J6994 

7121  7164  72067249 

7377^419  746217504 

7632767477177759 

78877930  7972  801 5 

8i42'8i85:8227827o 

8398,844o'8483  8525 

8653,869587388780 

8908 ,895o;899'i  9035 


68o5:6848 
7061  7104 
7317  7360 
7574  7616 
7830  7872 
80868129 
83428385 
85988641 
88548897 
9110  9153 
9366  9409 


9622 
9878 
1 34 
0390 
0646 
0902 
n58 
i4i4 
1669 
1925 
2181 
2437 
2692 
2948 

3204 

3459 
3715 


9665 
9921 
.177 
0433 
0689 

0945 
1200 
i456 
1712 
1968 
2224 
2479 
2735 
2991 
3246 
35o2 
3758 


3971U013 
4226U269 
44824524 
473714780 
4993  5o35 

5248:5291 

55o4;5546 
5759  58o2 
6oi5  6057 
627o|63i3 
65256568 
6781  6823 
7036,7079 
7291  7334 
75477^89 
78027845 
8057  8100 
8312  8355 
8568  8610 
[88238865 
9078  91 21 


•_l>"   \\v 


P.  Part 


Co-tangent  of  49  Degrees 

<  1"  2"  3"  4"  3"  6"  7"  8" 
\    \      9  13  17  21  26  30  34 


9" 
38 


Tangent  of  4 1  Degrees. 
v  I  40"  I 


9 
10 

1 1 
12 

r; 
14 
t5 
16 

17 
18 

l9 
20 
21 

22 
2'! 
24 

2  5 

26 

27 
28 
29 
3o 
3i 

32 

33 
34 
35 
36 

37 
38 
39 
4o 
4i 
42 

4'; 
44 
45 

4<i 
47 
48 

49 

5o 

5i| 

52 

53I 
54 

55 
56 

57 

59 


.939163 

9418 
9673 

9928 

.940183 
0439 

0694 
0949 

I204 
1459 

.941713 
I968 
2223 
2478 
2733 
2988 
3243 
3498 
3752 
4007 

.944262 

45i7 

4771 
5o26 
5281 
5535 
5790 
6o45 
6299 
6554 


7063 
7318 
7572 
7827 
8081 
8335 
8590 
8844 
9099 

.949353 
9608 
9862 

.950116 
0371 
0625 
0879 


9206 
9461 
9716 
9971 
0226 
0481 
0736 
0991 
1246 
i5oi 
i756 
2011 
2266 

2521 
2776 

3o3o 
3285 
354o 
3795 
4o5o 
43o4 
4559 
48i4 
5069 
5323 
5578 
5832 
6087 
6342 
6596 
685i 
7io5 
736o 
7614 
7869 
8i23 
8378 
8632 


9248 
95o3 
9758 
..i3 
0268 
o524 
0779 
io34 
1289 
i544 
1798 
2o53 
23o8 
2563 
2818 
3073 
3328 
3583 
3837 
4092 

4347 
4602 
4856 
5m 
5366 
5620 
5875 
6i3o 
6384 
6639 
6893 
7i48 
7402 
7657 

79" 
8166 
8420 
8675 
8929 
9184 
9438 
9692 


9291 '9333  9376  5 

9546y588;963i 
9801 I9843I9886 
56  .  .981.141 


o3n  03540396 
o566  0609  o65i 
0821  0864  6906:53 
1076  11191161152 
i33i  1374  i4:6!5i 
i586  1628  1671:50 
1841  i883  192649 
209621382181  48 
235i  2393  2436 
2606  2648  2691 
2861  2903  2945 
3ii5  3i58  32oo 
3379  34i3  3455 
3625  366713710 
388o3922'3965 
4i35  417714219 
4389  4432  4474 
4644  4686J4729 
4899  494114984 
5i53  5196  5238 
54o8  545i  5493 
5663  57o5  5748 
5917  5960 
6172 

6427  6469 
6681  6724 
6936  6978 
7190  7233  7275 
7445  74877530 
7699  7742  7784 
7954  7096  8039 
82088251  8293 
8463  85o5  8548 
8717  876018802 
8972  9014  9o56 
9141  9184  9226  9268931 1 
9396  9438  9480  9523J9565 
9650J9692  9735  9777  9819 
9904  9947  9989  . .  3 1  j . .  74 
0159  0201  0243  0286  o328 
o4i3  o455  0498  o54o,o582 
0667I0710  0752  0794  0837 
o92i|0964|ioo6jio49  1091 
n33i  176  i2i8|i26i'i3o3  i345 
i388;i43o|i472!i5i5|i557  1600 
1642  1684  1727  '17691181 1  i854 


6002 
6214  6257 
65n 

6766 
7021 


.951896  1938,1981 

2l5o  2193  2235 

24o5'2447J2489 
2659  2701  2743 


2023  2066  2Io8 
2277  2320  2362 

2532I2574  2616 
2786  2828  2870 


29 1 3 1  2955  29981 3o4o  3oSj  3 i 25 
3i6^i3209,3252l3294  3336  3379 
342i;3463;35o63548  35gi  3633 
3675  3718  376o  3802  3845  3887 
3929  3972  4oi4  4o56  4099  4 14 1 
4i83  4226'4268  43io4353  4395 


24 

23 
22 
21 

2  0 

«9 

[8 

17 
16 

i5 

1 4 
i3 
12 
1  i 
10 

9 

8 

7 
6 
5 
4 
3 
9 
I 


P.  Part 


80"    I  W      40"   30>|   90    to 

Co-tangent  of  48  nt«rrocs. 

I"     3"     -1"     V    ff*    7'     H'r 
8     13    17    21    2't    30    31 


{V 


E 


cc 


Logarithmic    Sines. 


Sine  of  42  Degrees. 

8 

Sine  of  43  Degrees. 

59 

0" 

10"  1  20"  j  30" 

40"  |  50" 

0" 

10"  1  20"  1  30" 

40" 

50" 

o 

9.S25511 

5534  5558  558i 

56o45628 

59 

0 

9.833783 

38o6  3828|385i 

3874 

3896 

I 

565i 

5675 

5698  5721 

57455768 

58 

1 

39i9 

3941 

39643986 

4009 

4o32 

53 

2 

5791 

58i5 

5838586i 

5885  5908 

57 

2 

4o54 

4077 

4099'4l22 

4i44 

4167 

57 

3 

5g3i 

5955 

59786001 

6o25 6o48 

56 

3 

4i89 

4212 

4234 

4257 

4280 

4302 

56 

4 

6071 

6095 

61186141 

6i656i88 

55 

4 

4325 

4347U370 

4392 

44 1 5 

4437 

55 

5 

6211 

6235 

62586281 

63o5  6328  54 

5 

446o 

4482  45o5 

4527 

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4572 

54 

e 

635i 

637563986421 

6444  6468  53 

6 

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4617 

464o 

4662 

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53 

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65846607 

52 

7 

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47^2 

4775 

4797 

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s 

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6654  6677  6701 

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5i 

8 

4865 

4887 

4910 

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9 

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9 

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9.826910 

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49 

IO 

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5 1 79  52oj 

5224 

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20 

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27 

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60"    J  50" 

40" 

30" 

20" 

10" 

3 

60"    |  50" 

40" 

30"  |  20"  |  10" 

a 

Co-sine  of  47  Degrees. 

Co-sine  of  46  Degrees. 

P. 

<  1" 

2"   3' 
5  7 

4" 
9 

5"  ( 
11  1 

"  7" 
4  16 

8" 
18 

9" 
21 

P. 

j 

1   1"  2"  3''  4"  5"  6"  7' 
rartj  0   4   7   9  n  13  K 

8" 

18 

9" 
20 

Logarithmic    Tangents. 


Tangent  of  42  Degrees. 


10"   20"   30"   40"   50" 


Tangent  of  43  Degrees. 


10"   20"   30"   40" 


i 

3 

3 
4 
5 
6 

7 

8 

9 
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1 1 

12 

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26 
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35 
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37 
38 
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7080 
7334 
7587 
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8347 
8600 
8854 
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9360 
9614 

10" 


Co-tangent  of  17  Degrees. 

(    1//     an     •»// 
PParti^     ~8     13 


9.969656  9698 


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P.  Part 


Co-tangent  of  46  Degrees 

:»"    4"    5"    6"    7"    8" 
13     17    21    2.'>    33    34 


<  1"    2" 
i    4      8 


08 

LOGARITHMIC  S  I  N  E  & 

!3 

Sine  of  44  Degrees. 

S3 

Sine  of  45  Degrees. 

1 

0" 

10" 

20"  |  30" 

40" 

50" 

0"    |  10" 

20" 

30" 

W 

50" 

0 

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739i 

7412  7433 

16 

43 

485o 

4870 

489i 

4911 

4932 

4953 

16 

44 

7454 

7476  7497 

75i8 

7539^561 

i5 

44 

4973 

4994 

5oi4 

5o35 

5o55 

5076 

i5 

45 

7582 

7603  7624 

7645 

76677688 

i4 

45 

5096,51 17 

5i37 

5i58 

5i78 

5199 

1 4 

46 

7709 

7730.7752  7773 

7794  7815 

i3 

46 

52i9'524o 

5260 

5281 

53oi 

5322 

i3 

47 

7836 h858  7879I 7900 

7921  7943 

12 

47 

534215363 

5383 

54o4 

5424 

5445 

12 

48 

7964 

7985  8006:8027 

8049  8070 

11 

48 

5465 

5485 

55o6 

5526 

5547 

5567 

11 

49 

8091 

8ii2!8i338i54 

8176  8197 

10 

49 

5588 

56o8 

5629 

5649 

5670 

5690 

10 

5o 

9.848218 

8239,826o8282 

83o38324 

9 

5o 

9 .  85571 1 

5731 

575i 

5772 

5792 

58i3 

9 

;  5i 

8345 

8366  8387'84o9 

843o845i 

8 

5i 

5833  5854 

58  74 

5895 

5915 

5935 

8 

52 

8472 

8493  85i4l8535 

85578578 

7 

52 

595615976 

5997 

6017 

6o38 

6o58 

7 

53 

8599 

86208641  8662 

86838705 

6 

53 

6078  6099  6119  6i4o 

6160 

6180 

6 

54 

8726 

874787688789 

8810  883i 

5 

54 

6201  6221 

6242  6262 

6282 

63o3 

5 

55 

8852 

887488958916 

89378958 

4 

55 

6323!6344 

63646384 

64o5 

6425 

4 

56 

8979 

9000  9021  9042 

9063  9085 

3 

56 

6446'6466  6486  65o7 

6527 

6547 

3 

57 

9106 

912719148  9169 

9190  9211 

2 

57 

6568j6588!66o9  6629  6649,6670 

2  ! 

58 

9232 

92.53  9274,9295 

o3i  6 9338 

1 

58 

6690  67 10  6731' 675  1  6771 '6792 

1 

59 

.  9359 

9380  9401  9422  9443  9464 

0 

59 

68i2|6832:6853  6873;6893;69i4 

0 

60" 

50"  j  40"  |  30"  |  20"  J  10" 

a 

60"    j  50"  j  40"  I  30"  |  20"  !  10" 

a 

Co-sine  of  45  Degrees. 

Co-sine  of  44  Degrees. 

P., 

„  .(  1"  2"  3"  4"  5"  6"  7"    8"  9"  1 
l&rl\   2   4   6   9  11  13  15  17  19  1 

P. 

C  1"  2"  3"  4"  5"  6"  7"  8"  9"    j 
lart(  2  4   6   8  10  12  14  17  19  j 

Logarithmic    Tangents. 


C9 


Tangent  of  44  Degrees. 


40"  I  50" 


Tangent  of  45  Degrees. 


0" 


10"   30"   30"   40"   5C 


O  i 

I 

3 

3 

4 

5 
6 

7 

8 

9 

109 
11 
1  a 

1 3 

i4 
1 5 

iG 

17 

18 

•y 
20 
21 
22 

23 

24 

25 

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27 

28 

29I 

3o|9 

3i 

32 

33 

34 
35 
36 

37 

38 

39 

409 

4i 

42 

43 

44 

45 

46 

47 

48 

49. 

5o  9 
5i 

52 

53 
54 
55 
56 

57 

58 
59 


.984837 
5090 
5343 
5596 
5848 
6101 
6354 


4879 
5i32 
5385 
5638 
5891 
6i43 
6396 


6607  6649 
6902 
7i54 


6860 
7112 
.987365 
7618 
7871 
8i23 
8376 
8629 
8882 
9i34 
9387 
9640 
.989893 
,990145 
0398 
o65i 
0903 


7407 
7660 
79i3 
8166 
84i8 
8671 
8924 
9177 
9429 
9682 
9935 
0187 
o44o 


4921 
5i74 
5427 
568o 
5933 
6i85 
6438 
6691 
6944 
7197 
7449 
7702 
7955 
8208 
846o 
87i3 
8966 
9219 
9471 
9724 
9977 

0230 

0482 


4964 

5216 

5469 

5722 

5975 
6228 

648o 
6733 


5oo6 
5259 
55n 

5764 


5o48 
53oi 
5553 
58o6 


601716059 
6270  63i2 


6523 
6775 


6986  7028 
7239  7281 
7491 17534 
7744' 


6565 
6817 
7070 
7323 
7576 


7786  7829 
8o39;8o8i 
8292^334 
8545;S587 
87978840 
9o5o  9092 
926119303^9345 
9613  9556-9598 
976698089850 


7997 
825o 
85o3 
8755 


0693  0735 


1 1 56  in 


0946)0988 
1240 
i493 
1746 
1999 


*9 

0272 

o524 
0777 
io3o 
1283 
i535 


204l 

25l|2293 

25o4  2546 
27572799 
3009  3o5i 
3262  33o4 
35i5  3557 
3767  38io 
4062 
43i5 
4568 


61  Lio3 
o3i4o356 
0567  0609 
0819  0861 
1072  in4 
i325ji367 
1577 1620 
18301872 

2o83  2125 

2336J2378 

a588a63o 

2841 J2883 
3og4  3i36 
33463388 
3599I3641 
3852;3894 
4io44i46 
435714399 
4610  4652 
48624905 
5n55i57 
5368J54io 
562o!5663 
58735915 
6126:6168 
63786421 
663i  6673 
6884^6926 
7136:7179 
7389*7431 
76427684 

78947937 

8105:81478189 
■v:  ;i  82738316  8358  84008442 
8484  "•J26.8568:86io!8652'8695 
8737  877918821  |8863J89o5:8947 
8989  9031  907491 16  91589300 
9242  9284  9326  9368|94i0  9453 
9495  9537  9579  962119663J9705 
9747  '97899832  J9874  9916995* 
v'~~    1  50"  I  ay  I  air  "~ 


1409  i45i 
:6G2  1704 
1 914  1956 
2167  2209 
992420  2462 
2672  2715 
292512967 

3l78  3220 
343  I  3473 

36833725 
3936  3978U020 
4189  423i U273 
444i  4483  45a6r- 
4694|4736  4778 U820 
.  994947:4989,503 1  j  5073 
5199^241  528415326 
5452  5494  5536j5578 
5705  5747  5789I5831 
5957'59996o42|6o84 
62io'6252  6294  6336 
G463'65o5  6547  6589 
67156757168006842 


696817010  7<ir)2 

7221   7263   7">nr) 

.997473:751 5  j7558 
7726J7768J810 
7979'8o2i|8o63 


7094 
7347 
7600 
7852 


nc 


P.I 


Co- tangent  of  45  Degrees. 

5"  6"  7"  W 


•"•'1  4 


j</  o'<  3'/ 

8  13  17  21  23  29  34 


10.000000  0042  Oo84  0126 
0253  0295  0337  0379 
o5o5  o547  0590  o632 
0758  0800  0842  0884 
ion  io53  1095  1137 
1263  i3o5  i348  1390 
i5i6  1 558  1600  1642 
1769  1811  i853  1895 
2021  2o63  2106  2148 
2274  23i6  2358  2400 

10.002527  2569  2611 
2779  2821  2864 
3o32  3074  3n6 
3285  3327  3369 
3537  3579  3622 
3790  3832  3874 
4o43  4o85  4i27 
429543374380 
4548  459o4632 
48oi  4843  4885 

io.oo5o53  5095  5i38 
53o6  5348  5390 
5559  56oi  5643 
58n  5854  5896 
6064  6106  6i48 
6317  6359  64oi 
656966126654 
6822  6864  6906 
7075  71 17  7159 
7328  7370  7412 

10.007580  7622  7664 
7833  7S75  7917 
8086  8128  8170 
8338  838o  8423 
85gi  8633*67$ 
8844  8886  8928 
9097  9139  9181 
9349  9391  9433 
9602 19644, 9686J9728 
9855I9897  9939  9981 

io.oioio7|Oi5o  0192  0234 
o36o:o4o2  o444 
o6i3  o655:o697 
0866  0908  0950 

II  l8  Il6o  1203 

1371  i4i3 i455 
i624'i666|i7o8 
1877J1919  1961 
2129  2171  2214 
2382|2424>466  25o9 
10.012635I2677  2719 
2888]293ol2972 
3i4o3i833225 
3393  3435  3477 


016810211  59 
0421  o463  58 
0674  0716157 
0926.0969J56 
11791221155 
i432i474p4 
1684  1727,53 
1937  1979  52 

2232 

2485 

2737 


2190 

2442 


2653  2695 
2906  2948^2990 


3i58 
34u 
3664 
3916 
4169 
4422 
4674 
4927 
5i8o 
5432 
5685 
5938 
6190 
6443 

6696 
6949 
7201 

7454 
7707 

7959 
8212 
8465 
8717 
8970 
9223 
9476 


0487 
o739 
0992 

1245 

1497 
1750 
2oo3 

2256 


2761 
3oi4 
3267 
3520 


3200  3243 
3453(3495 
37063748 


3g58 
42 1 1 
4464 


4ooi 

425343 

45o6  42 
4716-4759  4i 

4969  5on  4© 

5222(5264  39 

5474  55i7  38 
5727  5769  37 


5980  6022 
62336275 
6485|6527 
67386780 
6991  7033 
7243  7285 
7496:7538 

7749I7791 
8ooi,8o44 
82548296 
85078549 
87608802 
90i2'9o54|24 
9265  9307)23 
95i8'956o|22 
9770  9813  21 
a3  ..65  20 
027G  o3i8  19 
0529  0571  18 
0781  o8a3  17 
io34  1076  16 
1287  1329  i5 
1 54o  1 582 
1792  i834 
2045  2087 
2298  234o 
255i  259'J 
a8o3'a846 
3o56  3098 
3309  335 1 
3562 36o4 


3646  3688  3730(3772  38i 5  3S57 
389913941  3983U025U067  4109 
4i5a U194I4236  4278  432014362 
44o4  4447;4489  453i  4573  46i5 
4657  4699I474 1  478448a6  4868 
4910J4953  4994  5o36,5o79'5i2i 


m 


I   -JO"  '"  10 


Co-tangent  of  44  Degrees. 


i>  p   A  1"   -"    3"   4"   5"   °"  r 
1    lwr\   i      g     13    17    21    23    2f 


fi"    7"    6"    9' 
20    34    38 


70 

Logarithmic  Sines. 

A 
M 

1     Sine  of  46  Degrees. 

1 

II 

A 
2 

Sine  of  47  Degrees. 

1 

0" 

10"  |  20"  |  30" 

40" 

50" 

0" 

10"  |  20" 

30" 

40" 

50"  I 

o 

^9. 856934 

6954 

6975J6995 

7015 

7o36 

59 

0 

9.864127 

4l47J4l67 

4i86 

4206 

4226|5<f] 

I 

7o56 

7076 

70977117 

7i37 

7i58 

58 

I 

4245 

42654284 

43o4 

432  i 

4343 

58 

2 

7178 

7198 

72I9;7239 

7259 

7279 

5? 

2 

4363 

43834402 

4422 

4441 

446i 

57 

3 

73oo 

7320 

7340,7361 

738i 

74oi 

56 

3 

448 1 

45oo!4520 

4539 

4559 

4579 

56 

4 

7422 

7442 

74627482 

75o3 

7523 

55 

4 

4598 

46i8 

4637 

4657 

4676 

4696155 

5 

7543 

7563 

7584.7604 

7624 

7645  54 

5 

4716 

4735 

4755 

4774 

4794 

48i3  54 

5 

7665 

7685 

7705  7726 

7746 

7766 

53 

6 

4833 

4853 

4872 

4892 

491 1 

493 1 153 

7 

7786 

7807 

78277847 

7867 

7888 

52 

7 

495o 

4970 

4990 

5009 

5029 

5o4» 

l± 

8 

7908 

7928 

7948J7968 

7989 

8009 

5i 

8 

5o68 

5087 

5107 

5l20 

5i46 

5i65 

5i 

9 

8029 

8049 

8070  8090 

8110 

8i3o 

5o 

9 

5i85 

5204 

5224 

5244 

5263 

5283 

5o 

10 

g.858i5i 

8171 

8191:8211 

823i 

8252 

49 

10 

9.8653o2 

5322 

534i 

536i 

538o 

54oo 

49 

ii 

8272 

8292 

83i2'8332 

8353  8373 

48 

1 1 

5419 

5439 

5458 

5478 

5497 

55i7 

48 

12 

8393 

84i3 

84338454 

8474  8494 

47 

12 

5536 

5556 

5575 

5595 

56i4 

5634 

47 

i3 

85i4 

8534 

8554,8575 

859586i5 

46 

i3 

5653 

5673 

5692 

5712 

573i 

575i 

46 

i4 

8635 

8655 

8675,8696 

8716 

8736 

45 

i4 

5770 

579o 

5809 

5828 

5848 

5867 

45 

i5 

8756 

8776 

8796|88i7 

8837 

8857 

44 

i5 

5887 

5906 

5926 

5945 

5965 

5984 

44 

16 

8877 

8897 

89178937 

8958 

8978 

43 

16 

6oo4 

6023 

6042 

6062 

6081 

6101 

43 

17 

8998 

9018 

90389058 

9078  9098 

42 

!7 

6120 

6i4o 

6i5g 

6179 

6198 

6217 

42 

18 

9119 

9i39 

91599179 

9199  9219 

4i 

18 

6237 

6256 

6276 

6295 

63i5 

6334 

4i 

*9 

9239 

9259 

9279  9300 

9320 

9340 

4o 

J9 

6353 

6373 

6392 

64i2  643i 

645o 

4o 

20 

9.859360 

938o 

9400  9420 

944o 

9460 

39 

20 

9.866470 

6489 

65o9 

6528,6547 

6567 

39 

21 

9480  9501 

9521  9541 

9561 

9581 

38 

21 

6586 

6606 

6625 

6644 

6664 

6683 

38 

22 

9601  9621 

9641  9661 

9681 

9701 

37 

22 

6703 

6722 

6741 

6761 

6780 

6800 

37 

23 

9721  9741 

9761  9781 

9802 

9822 

36 

23 

6819 

6838 

6858 

6877 

6896 

6916 

3C 

24 

9842  9862 

9882  9902 

9922 

9942 

35 

24 

6935 

6954 

6974 

6993 

7013 

7032 

35 

25 

996219982 

. .  .2 ' . .22 

..42 

..62 

34 

25 

7o5i 

7071 

7090 

7109 

7129 

7i48 

34 

26 

9.860082 

0102 

0122  0142 

0162 

0182 

33 

26 

7167 

7187 

7206 

7225 

7245 

7264 

33 

27 

0202 

0222 

0242  0262 

0282  o3o2 

32 

27 

7283 

73o3 

7322 

734i 

736i 

738o 

32 

28 

0022 

o342 

o362  o382 

0402  o422 

3i 

28 

7399 

7419 

7438 

7457 

7476 

7496 

3i 

29 

o442 

0462 

0482  o5o2 

0522 

o542 

3o 

29 

75i5 

7534 

7554 

7573 

7592 

7612 

3o 

3o 

9,860562 

o582 

0602  0622 

0642 

0662 

29 

3o 

9.867631 

765o 

7669 

7689 

7708 

7727  29 

3i 

0682 

0702 

0722  0742 

O762 

0782 

28 

3i 

7747 

7766 

7785 

7804 

7824784328 

32 

0802 

0822 

o842'o862 

08820902 

27 

32 

7862 

7882 

7901 

7920 

79397959l27 

33 

0922 

0941 

0961  0981 

IOOI  1021 

26 

33 

7978 

7997 

8016 

8o36 

8o55 

807426 

34 

1041 

1061 

1081  IIOI 

1 121 II  i4i 

25 

34 

8o93 

8n3 

8i32 

8i5i 

8170 

8190125 

35 

1 161 

1181 

1201  1221 

I24o  I26o 

24 

35 

8209 

8228 

8247 

8267 

8286 

83o5  24 

36 

1280 

i3oo 

i32o  i34o 

i36o 

i38o 

23 

36 

8324 

S343 

8363 

8382 

84oi 

8420|33 

3? 

i4oo 

1420 

i439'i459  1479 

1499 

22 

37 

844o 

8459 

8478 

8497 

85i6 

8536 

22 

38 

1519 

i539 

i559  1 679  099 

1618 

21 

38 

8555 

8574 

8593 

8612 

8632 

865i 

21 

39 

i638 

i658 

1678  1698 

1718 

i738 

20 

39 

8670 

8689 

8708 

8728 

8747 

8766 

20 

4o 

9.86:758 

1777 

17971817 

i837 

1857 

x9 

4o 

9.868785 

8804 

8823 

8843 

8862 

8881 

19 

4i 

1877  1897 

1916  1936 

1956 

1976 

18 

4i 

8900 

8919 

8939 

8958 

8977 

8996 

18 

42 

1996  2016 

2o35  2o55 

2075 

2095 

r7 

42 

9015 

9034 

9o53 

9o73 

9092 

9111 

l7 

43 

2Il5 

2i35 

2i54  2174 

2194 

22l4 

16 

43 

9i3o 

9149 

9168 

9188 

9207 

9226 

16 

44 

2234 

2254 

2273  2293 

23i3 

2333 

i5 

44 

9245 

9264 

9283 

9302 

9321 

9341 

1 5. 

45 

2353 

2372 

2392  2412 

2432 

2452 

i4 

45 

9360 

9379 

9398 

9417  9436 

9455 

iA 

46 

2471  2491 

25i  1  253i 

255i 

2570 

i3 

46 

9474 

9494 

95 1 3 

9532  9551 

957o 

i3 

47 

2390  2610 

263o  265o 

2669 

2689 

12 

47 

9589 

9608 

9627 

9646 

9665 

9685 

12 

48 

270912729127482768  2788  2808 

1 1 

48 

9704 

9723 

9742 

9761 

9780 

9799 

11 

49 

2827  2847  2867l2837  2906 

2926 

10 

49 

9818 

9837 

9856 

9875  9894 

99i4|io 

5o 

9,862946 

2966,2985^005 

3o25 

3o45 

9 

5o 

9.869933 

99529971 

9990  ...9 

..28|  9 

5 1 

3o64 

3o84  3io4i3i24 

3i43 

3i63 

8 

5i 

9.870047 

oo66,oo85 

OI04  OI23 

01421  8 

52 

3i83 

32o3 

3222  3242 

3262 

3281 

7 

52 

0161 

0180  0199 

02i8j0238 

0257  7 

53 

33oi 

332i 

334i 

336o 

338o 

34oo 

6 

53 

0276 

0295  o3i4 

o333o352 

0371 

6 

54 

34i9 

3439 

3459 

3478 

3498 

35i8 

5 

54 

0390 

0409  0428 

o447jo466 

o485 

5 

55 

3538 

3557 

3577 

3597 

36i6 

3636 

4 

55 

o5o4 

o523  o542 

o56i  o58o 

0599 

4 

56 

3656 

3675 

3695 

37i5 

3734 

3754 

3 

56 

0618 

o637jo656 

0675,0694 

0713 

3 

57 

3774 

3793 

38i3 

3833 

3852 

3872 

2 

57 

0732 

0751  0770  0789  0808 

0827 

2 

58 

3892 

3911 

3g3i 

3951 

397o 

3990 

1 

58 

o846 

o865  o884  0903  0922 

0941 

1 

59 

4oio 

4029 

4049 

4069 

4o88 

4io8 

0 

59 

0960  0979^998 j  1 01 7' 1  o36  io54 

0 

60"   1  50" 

40" 

30"  |  20" 

10" 

2 

60"    |  50"  |  40"  1  30"  j  20"  i  10" 

T 

Co-sine  of  43  Degrees. 

Co-sine  of  42  Degrees. 

3 

r. 

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Co-sine  of  41  Degrees. 

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P. 

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Logarithmic    Tangents 


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Co-sine  of  39  Degrees. 

Co-sine  of  38  Degrees. 

v   p   <  1"  2"  3"  4"  5"  6"  7"  8"  9" 
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Co-tangent  of  36  Degrees. 

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1 

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• 

Co-sinc  of  35  Degrees. 

Co-sine  of  34  Degrees. 

a 

r. 

p  .<  1"  2"  3"  4"  5"  6"  7"  8"  9"  II  „ 
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C  1"  2"  3"  4"  5"  6"  7"  8"  9"  , 
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Logarithmic 

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79 

1 — 

s 

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s 

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30"  j  20"  j  10" 

= 

Co-sine  of  33  Degrees. 

Co-sine  of  32  Degrees. 

a 

P. 

p  .51"  2"  3"  4"  5"  6"  7"  8"  9" 
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P  P  t51"  2"  3"  4"  5"  6"  7"  8"  9" 
r.rart^  !   3   4  5   7   8   9  11  12 

Logarithmic  Tangents 


81 


Tangent  of  56  Degrees. 


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6101  6147  6193  6239  6285  633 1 
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7206  7252  7298  7344,7390  7 ;  ',7 

60"         io«  ,  30"  I  30"   icy* 


Co-tangent  of  33  Degrees. 


p  r-.rtJ  l"   ~"   3"  '«"  5"  *>"   '"   s'  ;'" 

r-la"(  5   9  14  18  23  27  32  37  11 


Tangent  of  57  Degrees. 


10. 187483  7529 
7759  7805 
80368082 
83i38359 
859o|8636 
8866.8913 
914319190 
94209467, 
96989744 
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30"       40" 


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898  7944.7990 


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1732  177811824,1871 
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2565  2612  2658  2704 
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8i38'8i85  82328278  2: 

84i8  8465a5n  8558  20 

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8977  9024  9070  91 17 

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0937,0983 

1217  1263 

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5 


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io3o  1077 
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1 59 1  1637 
1871  1918 
201  2198 


a338  2385  2432  2479 

26i9'a666|27i3  3759 

2806I2853I2900  2947  2993  3o4o 

3iSi  3227  3a74|33ai 

3461  35oS,3555  36oa 
3742  3789  3836  3883 


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P.  Part 


Co-tangent  of  :l*i  Degrees. 

3"   r   5"  6"  7'  h' 


v: 


I" 


1!)    23    28    33.  37    42 


32 

L 

OG  A  III 

riiMic  Sini 

:s. 

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1 

Sine  of  58  Degrees. 

B 

Sine  of  59  Degrees. 

I 

0" 

10"  1  20"  j  30"  |  40"  1  50" 

0" 

10" 

20" 

30" 

40" 

50" 

1 

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GO"    1  50"  j  40"  |  30"  |  20"  I  10" 

.5° 

60"    |  50"  j  40"  j  30"  1  20"  |  10" 

S3 

Co-sine  of  3 1  Degrees. 

Co-sine  of  30  Degrees. 

P. 

VnrA  1"  2"  3"  4"  5"  6"  7"    8"  9" 
rvn[   1   3   4   5   6   8   9  10  12 

pp  .Cl"    2"    3"  4"  5"  6"  7"   8"   9" 
1.  rait  j  1   2   4   5   6   7   9  10  11 

Logarithmic    Tangents. 


83 


Tangent  of  58  Degrees. 


40"  I  50" 


Tangent  of  59  Degrees. 


50" 


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a 
3 
4 

5 
6 

7 

8 

9 

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i 

Sine  of  60  Degrees. 

c 

s 

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60"    |  50" 

40"  |  30"  |  20" 

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c 

60"    1  50"  j  40"  |  30"  1  20"  1  10" 

j 

Co-sine  of  29  Degrees. 

Co-sine  of  28  Degrees. 

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2 

„  .(  1"  2"  3"  4"  5"  6"  7"  8"  9" 
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.  .-  - ..... 

Logarithmic    Tangents. 


85 


Tangent  of  60  Degrees. 


10"  I  20"   30" 


Tangent  of  6 1  Degrees. 


v 


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0879  0930  1 1 


n8';  1233 

i486  i537 
1790  is4i 
2oy4  2i45 
2347  2398  -449 
265i  2702  2755 
2955  3oo6  3o57 
326oi33io  336i 
3564!36i5  3666 
3869139 1 9  3970 
417342244275 


5"  6"  ?"  8"  9" 
2.')  30  3j  40  4.r» 


86 


Logarithmic    Sines. 


Jj 

Sine  of  62  Degrees. 

3 

Sine  of  03  Degrees. 

1 

0" 

10"  |  20"'  1  30"  |  40" 

50" 

0" 

10"  |  20"' 

30" 

40" 

5(1" 

1 

o 

9.945935 

5946^957  5969  5980 

599i  59 

O 

9.949881 

9892I9902 

99i3 

9924 

9935 

59 

I 

6002 

6013,6024  6o366o47 

6o5858 

I 

9945 

9956  9967 

9977 

9988 

9999 

58 

2 

6069 

6080  6092  61  o3, 61 14 

6i25 

57 

2 

9.950010 

0020  po3i 

0042  oo52 

oo63 

57 

3 

6i36 

61476159  6170,6181 

6192 

56 

3 

0074 

0084  0095 

0106 

OII7 

0127 

56 

4 

6203 

6214  6226  6237,6248 

6209 

55 

4 

oi38 

0149  0159 

0170 

Ol8l 

0191 

55 

5 

6270 

6281  62936304  63i5 

6326|54 

5 

0202 

02i3  0224 

0234 

0245 

0256 

54 

6 

6337 

6348  6359  637X 

6382 

639353 

6 

0266 

0277  0288 

0298 

0309 

0320 

53 

7 

64o4 

6415  6426,6437 

6449 

646o52 

7 

o33o 

o34i p352 

o362 

0373 

o384 

53 

8 

6471 

6482  6493^504 
6549  656o  6571 

65i5 

6526 

5i 

8 

0394 

o4o5p4i6 

0426 

0437 

o448 

5i 

9 

6538 

6582 

6693 

5o 

9 

o458 

04690480 

0490 

o5oi 

o5i2 

5o 

IO 

9.946604 

66i5(66276638 

6649 

6660 

49 

10 

9.950522 

o533  o544 

o554 

o565 

0576 

49 

ii 

6671 

668266936704 

67i5 

6726 

48 

ii 

o586 

05970607 

0618 

0629 

0639 

48 

12 

6738 

6749*67606771  6782 

679347 

12 

o65o 

0661I0671 

0682 

0693 

0703 

47 

i3 

68o4 

68156826,68376849 

686o46 

i3 

0714 

0724 

0735 

0746 

0756 

0767 

46 

i4 

6871 

6882  6893^9046915 

692645 

14 

0778 

0788 

0799 

0809 

0820 

o83i 

45 

i5 

6937 

694869S9  6970J6982  6993 

44 

i5 

o84i 

o852 

0862 

0873 

0884 

0894 

44 

16 

7004 

7oi5  7026,7037 

7048 

7o59 

43 

16 

0905 

0915 

0926 

o937 

0947 

og58 

43 

17 

7070 

7081  7092  7103 

7114 

7125 

42 

17 

0968 

0979 

0990 

1000 

IOII 

1021 

42 

18 

7i36 

7147  7i58  7170 

7181 

7192 

4i 

18 

io32 

io43 

io53 

1064 

1074 

1 08  5 

4x 

J9 

7,203 

7214  722517236 

7247 

7258 

4o 

l9 

1096 

1 1 06 

1117 

1127 

n38 

xi48 

4o 

20 

9.947269 

7280  7291  7302 

73i3 

7324 

39 

20 

9. 951169 

1 1 70 

1180 

1 191 

1201 

1212 

39 

21 

7335 

734673577368 

7379 

7390I38 

21 

1222 

1233 

1244 

12S4 

1265 

1275 

38 

22 

7401 

7412  7423,7434 

7445 

7456  37 

22 

1286 

1296 

1 307 

1317 

1328 

1339 

37 

23 

7467 

7478  7489  7500 

75n 

7522  36 

23 

I  349 

ll36o 

1370 

i38i 

1391 

l402 

36 

24 

7533 

754575567567 

7578 

7589 

35 

24 

1412 

i423 

i434 

1 444 

i455 

i465 

35 

25 

7600 

7611  7622J7633 

7644 

7655 

34 

25 

l476 

i486 

1497 

1 507 

i5i8 

1528 

34 

26 

7665 

7676  7687 

7698 

7709 

7720 

33 

26 

i539 

1 549 

i56o 

1570 

i58i 

1591 

33 

27 

773i 

7742  7753 

7764 

7775 

7786 

32 

27 

1602 

i6i3 

1623 

1 634 

1 644 

i655 

32 

28 

7797 

7808  7819 

783o 

7§4i 

7852 

3i 

28 

1665" 

1676 

1686 

1697 

1707 

1718 

3i 

29 

7863 

78747885 

7896 

7907 

7918 

3o 

29 

1728 

1739 

1749 

1760 

1770 

1781 

3o 

3o 

9.947929 

79407951 

7962 

7973  7984 

29 

3o 

9.951791 

1802 

1812 

1823 

i833 

1844 

29 

3i 

7995 

800680178028 

8o38,8o49 

28 

3i 

i854 

i865 

i875 

1886 

1896 

1907 

28 

32 

8060 

8071  80828093 

8io48n5 

27 

32 

1917 1928 

1938 

1949 

i959 

1969 

27 

33 

8126 

8i37'8i48  8i59 

81708181 

26 

33 

1980  1990 

2001 

2011 

2022 

2032 

26 

34 

8192 

8203  8213  8224 

8235  8246 

25 

34 

2o43 

2o53 

2064 

2074 

2o85 

2095 

25 

35 

8257826882798290 

83oi 

83i2 

24 

35 

2106 

2116 

2126 

2137 

2147 

2i58 

24 

36 

8323  8334  8344  S355 

8366 

8377 

23 

36 

2168 

2179 

2189 

2200 

2210 

2221 

23 

37 

8388  83998410  8421 
8454  8464  8475  8486 

8432 

8443 

22 

37 

223l 

2241 

2252 

2262 

2273 

2283 

22 

38 

8497  85o8 

21 

38 

2294 

23o4 

23l4 

2325 

2  335 

2346 

21 

39 

85i9  8530*854x8552 

8562  8573 

20 

39 

2356 

2367 

2377 

2387 

2398 

2408 

20 

4o 

9-948584  8595  86o6J86i7 

86288639 

*9 

4o 

9.952419 

2429 

244o 

245o 

2460 

2471 

l9 

4i 

865o 

86608671  8682 

86938704 

18 

4i 

2481 

2492 

2502 

25l2 

2523 

2533 

l8 

42 

87i5 

872687368747 

87588769 

'7 

42 

2544 

2554 

2565 

2575 

2585 

2596 

17 

43 

8780 

879i'88o2  8812 

88238834 

16 

43 

2606 

2617 

2627 

2637 

2648 

2658 

16 

44 

8845 

8856,88678878 

8888,8899 

i5 

44 

2669 

2679 

2689 

2700 

2710 

2720 

i5 

45 

8910 

8921,89328943 

8954,8964 

i4 

45 

2731 

2741 

2752 

2762 

2772 

2783 

i4 

46 

8975 

8986,8997  9008 

9019:9029 

i3 

46 

2793 

2803 

2814 

2824 

2835 

2845 

i3 

47 

9040 

9o5i  9062  9073 

9083  9094 

12 

47 

2855 

2866 

2876 

2886 

289.7 

2907 

12 

48 

9io5 

9116  9127  9138 

91489159 

11 

48 

2918 

2928 

2938 

2949 

2959 

2969 

11 

49 

9170 

9181  9192,9202 

9213  9224 

10 

49 

2980 

2990 

3ooo 

3dn 

302I 

3o3i 

IQ 

5o 

9.949235 

9246  9256  9267 

9278  9289 

9 

5o 

9.953042 

3o52 

3o62 

3073 

3o83 

3093 

9 

5i 

9300 

9310  9321  9332 

9343  9354 

8 

5i 

3io4 

3n4 

3i24 

3i35 

3i45 

3i55 

8 

52 

9364 

9375  93869397 

9408  9418 

7 

52 

3i66 

3i76 

3i86 

3197 

3207 

3217 

7  i 

53 

9429 

94409451  9462 

9472^483 

6 

53 

3228 

3238 

3248 

3259 

3269 

3279 

6 

54 

9494 

95o5  o5i5j9526 
9569'958o  9591 

9537;9548 

5 

54 

3290 

33oo 

33io332i 

333i 

334i 

5 

55 

9558 

9602  9612 

4 

55 

3352 

3362 

3372  3382  33g3  34o3 

4 

56 

9623 

9634  9645.9655 

9666  9677 

3 

56 

34x3  3424  3434  3444J3455  3465 

3 

57 

9688  9698  9709  9720  9731  9741 

2 

57 

3475  3485  3496,35o6,35i6'3527 

2 

58 

9752  9763'9774;9784i9795  9806 

1 

58 

3537  3547  3557  3568  3578  3588 

1 

591 

9816  9827  9838  984919859  9870 

0 

59 

3599  3609  3619  3629  364o  365o  0 

60"    |  50"  i  40"  |  30"  |  20"  |  10" 

d 

60"    |  50"  |  40"  i  30"  j  20"  |  10"  |  e- 

Co-sine  of  26  Degrees.     3 

Co-sine  of  27  Degrees. 

S||   I 

P. 

Pn  i   1"  2"  3"  4"  5"  6"  7"  8"  9"   „ 
rari}  12345789  10   1- 

c  l»  o"  3"    4"  5"  C"  7"   8"   9" 
rart}  12345G789 

Logarithmic    Tangents. 


87 


Tangent  of  G2  Degrees. 


o 
i 

2 

3 
4 
5 
6 

7 

8 

9 
io 
ii 

I! 

i3 
i4 
i5 
16 

17 


21 

22 
23 
2^ 
25 
2fi 
27 
25 

£9 
3o 
3 1 

32 

33 

34 
35 
36 

37 
38 
39 
4o 
4i 
42 
4 '5 
44 
45 
46 
47 
48 

49 

5o 
5i 

52 

53 

54 
55 
56 

r>7 
5s 

59 


.274326 
463o 
4935 
524o 
5546 
585i 
6i56 
6462 
6768 
7o73 

,277379 
7685 

799 1 
8298 

86o4 
8911 
9217 
9524 
9831 
280138 
28o445 
0752 


4376 
468i 
4986 
5291 
5597 
5902 
6207 
65i3 
6819 
7124 
743o 
7736 
8o43 
8349 
8655 
8962 
9268 
9575 
9882 
0189 
0496 
0804 


1060  in  1 
1 367  1419 
1675  1726 
1983  2034 

2342 

265o 
2958 


::>. 


2291 

2599 

2907 

32i5|3266 
a835233575 

38323883 

4i4o  4192 

4449  "" 

4?58 

5067 

5376 

5686 

5995 

63o4 
286614 

6924 

7234 

7544 

7854 

8i64 

8475 

8785 

9096 

9407J9458 
289718  9769 
290029  0081 

o34o  0392 

o65r  0703 

0963  ioi5 

1274  1 326 
,  i58G  i638 

1898  1950 

22JO  2262 
2522  2574 


4529 

4834 
5i39 
5444 
5749 
6o55 
636o 
6666 
6971 
7277 
7583 
7889 
8196 
85o2 
8809 
911? 
9422 
9729 
36 
o343 
o65o 

°957 
1265 
1572 
1880 
2188 
249G 
2804 

3lI2 

3421 

3729 

4o38 

4346 

4655 

4964 

5273 

5582 

5892 

6201 

65n 

6821 

7i3o 

744o 

775i 

8061 

837i 

8682 

8992 

93o3 

9614 

9925 

0236 

o547 

o85 

1 1 70 

1482 

1794 

2106 

2418 

2730 

Co-tangent  of  27  Degrees 


45oi 
4810 
5i  19 
5428 
5737 
6o46 
6356 
6666 
69751 
7285 
7595 
7906 
8216 
8526 
8837 
9U8 


30" 


4427 
4732 
5o37 
5342 
5647 
5g53 
6258 
6564 
6870 
7i75 
748i 

7787 
8094 
84oo 
8706 
9013 
9320 
9626 
9933 
0240 
o548 
o855 
1162 
1470 
1777 
2o85 
2393 
2701 
3009 
33i8 
3626 
3935 
4243 
4552 
4861 
5170 

5479 
5789 
6098  6i5o 
64o86459 
6717  6769 


4478 
4783 
5o88 
5393 
5698 
6oo4 
6309 
66i5 
6920 
7226 
7532 
7838 
8i45 
845 1 
8757 
9064 
937i 
9678 
9984 
0292 
0599 
0906 

I2l4 
l52I 

1829 
2137 
2445 
2753 
3o6i 
3369 
3678 
3986 

95 
46o4 
4gi3 

22 
553 1 
584o 


50" 


7027 
7337 
7647 


7079 
7389 
7699 


7957  8009 
82688319 
8578863o 
88898941 
91999251 
951019562 
9821  9873 
Ol32  pi84 

o444  0496 
0755  0807 


1066 
1 378 
1690 
2002 

23l4 

2626 


1118 

i43o 
1742 

2054 
2366 
2678 


00"  i  40"  I  30" 


458o 
4885 
5190 
5495 
58oo 
6io5 
64n 
6717 
7022 
7328 
7634 
794o 
8247 
8553 
8860 
9166 
9473 
9780 
..87 
0394 
0701 
1009 
i3i6 
1624 
1931 
2239 
2547 
2855 
3i64 
3472 
3780 


4398 
4707 
5oi6 
5325 
5634 
5943 
6253 
6562 
6872J19 
7182  18 
7492  17  |j  42 
7802I16II43 
8n3  i5 
8423  14 
8733  i3 
9044  12 
9355j  1 1 
9666^0  4y 
9977  9i5o 


Tangent  of  G3  Degrees. 


10.292834 
3i46 
3459 


10"   20" 


2886 
3199 

35u 


3772  3824 
4o84  4i37 


4397 
4710 
5024 
5337 
565o 


4449 
4763 
5076 
5389 
5703 


2938 
325i 
3563 
3876 
4189 
45o2 
48i5 
5128 
544 1 
5755 


10.29596460166068 
627863306382 
6591  66446696 


6905  6958  7010 
7219  7272  7324 
7534  7586  7638 
7848  7900  7953 
8i63  8215  8267 
8477  853o  8582 
8792  8845  8897 

10.299107  9i59'92i2 
9422  9475J9527 
973797909842 

io.3ooo53  oio5  01 58 
o368  0421  o473 
068407360789 
0999' 1052  1  io5 
1 3i  51 1 368  1421 
i63i  1684  1737 
1947  2000  2o53 

10.302264  23162369 
258o  2633  2686 
2897  2950  3002 
32i3  32663319 
353o  3583  3636 
384739003953 
4164U2174270 
448245354588 
4799  4852U905 
5ii7!5i7oJ5223 
.3o5434!5487!554o 

5752|58o5  5858j59i i|5964 
6070  61 23j6i 76:6229:6282 
6388,644i  6494  6547'66oo 
6707  676o68i3  6866  6919 
7025  7078^131  7184  7237 
7344  7397  745o75o3  7556 
7662  7715,7768  7822  7875 
7981  8o34!8o878i4i  8i94 
83oo8353  84o6  846o85i3 

io.3o86i9  8672  8726,8779  8832 
8938  8992:9045  9098  91 5i 
9258  931 1  b364  9418  9471 
9577(963i  9684:97379790 
9897  995o  . .  .4  .  .57  . 1 10 

1  o.3 1 02 1 7  0270  0324,0377^430 
0537^590  o644  0697  0750 
0857,0910  0964  1017  1070 
1177  I23i  1284  1337:1391 
1498  1 55 1  if>o5  i658  171  1 


2990 
33o3 
36i5 
3928 
424i 
4554 
4867 
5i8o 
5494 
5807 
6121 
6434 
6748 
7062 

7377 
7691 
8oo5 
832o 
8635 

8949 
9264 
958o 
9895 
0210 
o526 
o84i 
1 157 
i473 
1789 
2106 
2422 
2738 
3o55 
3372 
3689 
4oo6 
4323 
464o 
4958 
5276 
55g3 


3o42 
3355 
3667 
3980 
4293 
46o6 
4919 

5232 

5546 
5859 
6173 
6487 
6801 
71 15 
7429 
7743 
8o58 
8372 
8687 
9002 
93i7 
9632 

9947 
0263 
o578 
0894 
1210 
i526 
1842 
2i58 
2475 
2791 
3io8 
3425 
3742 
4059 
4376 
4693 
5on 
5328 
5646 


3og4 
34»7 
3720 
4o32 
4345 
4658 
4971 
5285 


5598  5i 

5gi2 

6225 

6539 

6853 

7167 

748i 

7796 

8110 

8425 

8740 

9054 

937° 
9685 


o3i5 

o63i 

0947 

1263 

i579 

1895 

2211 

2527 

2844 

3i6i 

3478 

3794I25 

4lI2  24 

442923 
474622 
5o64  21 
538i  20 
5699  19 
6017  18 
6335i7 
6654  1 6 
6972  i5 
7290  14 
7609!  1 3 
12 
1 1 

IO 


7928 
8247 

8566 
S885 
9205 
9524 
9844 
.164 
o484 
0804 
1124 
i444 
1765 


40"   30" 


Co-tan<jent  of  20  Degrees. 


P.  Part 


S  1"   2" 
I  5     10 


15 


4"    5"    6"    7" 
21    2G    31    3G 


8"    !)" 
41    46 


P.  Part 


1  ' 


'2"    3"    4"    5"    6"    7"    8"    9" 
11     16    21    S6    32    37    42    47 


88 


L  O  G  A  K  I  T  H  M  I  C      IS  I  N  E  S. 


Sine  of  64  Decrees. 


Sine  of  G5  Degrees. 

"40" 


30" 


09. 963660 
3722 
3783 


36703681 


3691 
3753 

38i4 
3876 

3937 


3732  3742 

3794  38o4 
3845J3855  3865 
39063917  3927 
396839783988.3998 
402914039  4o5o,4o6o 
40904101  4"i  U121 
4I521 
42134223 


3701 
3763 
3824 
3886 
3947 


3712 
3773 
3835 
3896 
3957 


4009  4019 
4070  U080 


10:9.954274 


1 1 
12 
i3 

1 4 

1 5 
16 

17 

18 

'9 

20 

21 

22 
2  3 
24 
25 

26 

27 
28 
20 
3o 

3i 

32 

33 
34 
35 
36 

37 
3* 
39 

4o 
4i 

42 
43 
44 
45 
46 
47 

48 

49 
5o 

5i 

52 

53 
54 
55 
56 

57 
58 

5q 


4335 
4396 

4457 

45i8 

4579 

464o 

4701 

4762 

4823 
9.954883 

4944 

5oo5 

5o65 

5 1 26 

5i86 

5247 

53o7 

5368 

5428 
9.955488 

5548 

5609 

5669 

5729 

5789 

5849 

5909 

5969 

6029J6039 
9.956089  6099 

6i486i58 

62086218 

6268!6278 

6327:6337 

63876397 

6447  6457 

65o6  65i6 

6566  6575 

66256635 
9.956684  6694 

67446754 


4162  4172  4182 
4233!4243 
4284 
4345 
44o6 
4468 
4529 

4589 

465o 

4711 

4772 
4833 

4894 
4954 
5oi5 
5075 
5i36 
5196 
52S7 
53i7 
5378 


4294  43o5 
43564366 

4417.4427 
447*4488 
4539U549 
4600  4610 
4661  4671 
4721J4732 
4782  4792 
48434853 
49044914 
49644974 
5o25  5o35 
5o86  5096 
5i465i56 
5207  5217 
5267  5277 
532.75337 
5388  5398 
5438154485458 
549855o8'55i8 


4i3i 
4192 
4254 
43i5 
4376 
4437 
4498 
4559 


4i4i 

4203 

4264 

4325 
4386 

4447 
45o8 
4569 


462o|463o 


468i 
4742 
4802 
4863 
4924 


4691 
4752 
48i3 
4873 
4934 


5559 
5619 
5679 
5739 
5799 
5859 
59i9 
5979 


68o3 
6862 
6921 

6981 
7040 
7099 
7i58 
7217 


68i3 
6872 
6931 
6990 
7o5o 
7109 
7168 
7227 


5569  5579 
5629  5639 
5689  5699 
5749  5759 
5809  5819 
5869  58791 
5929  5939 
5989  5999 
6049  6059 
61086118 
61686178 
6228  6238 
6288*6298 
6347|6357 
6407  6417 
64666476 
6526'6536 
6585,6595 
6645|6655 
6704J6714 
6763^6773 
68236833 
6882!6892 
694 1 16951 


49854995 
5o455o55 

5io6  5n6 

5  i66i5i  76 

5227  5237 
5287  5297 
53485358 
54o8  54i8 
54685478 
55285538 
5589  5599 
5649  5659 
570915719 
5769J5779 
5829|5839 
5889  5899 
5949  5959 
6009,6019 
6069  6079 
6128  6i38 
61886198 
62486258 
63o8  6317 
63*676377 
6427  6437 
6486  6496 


7000 
7o59 
7118 
7177 
7236 


7010 
7069 

7128 
71871 
7246 


6546 
66o5 
6665 
6724 
6783 
6843 
6902 
6961 
7020 
7079 
7i38 
7197 
7256 


6556 
66i5 
6674 
6734 
6793 
6852 
6912 
6971 
7o3o 
7089 
7i48 
7207 
7266 


9.957276 
7335 
7393 
7452 
75n 
757o 
7628 
7687 
7746 
7804 

9.957863 
7921 

7979 
8o38 
8096 
8i54 
8213 
8271 
8329 
8387 
9.958445 
85o3 
856i 
8619 
8677 
8734 
8792 
885c 


8965 

9.959023 
9080 
9i38 
9195 
9253 
9310 
9368 
9425 
9482 
9539 

9.959596 
9654 
9711 
9768 
9825 
9882 
9938 
9995 

9.960052 
0109 

9.960165 
0222 
0279 
o335 
0392 
0448 
o5o5 
o56i 
0618 
0674 


7286 
7344 
74o3 
7462 
7521 

7579 

7638 
7697 
7755 
7814 
7872 
7931 

7989 
8047 
8106 
8i64 
8222 
8280 
8339 
8397 
8455 
S5i3 
8571 
8628 
8686 
9744 
8803 
8860 
8917 
8975 
9033 
9090 
9i48 
9205 
9262 
9320 

9377 
9434 
9492 
9549 
9606 
9663 
9720 

9777 
9834 
9891 
9948 
...5 
0061 
0118 
0175 

0232 
0288 
0345 

o4oi 
o458 
o5i4 
0571 
0627 
o683 


7295 
7354 
74i3 
7472 
753i 
7589 
7648 
7707 
7765 
7824 
7882 
7940 

7999 

8057 
8n5 
8i74 
8232 
8290 


84o6 
8464 

8522 

858o 
8638 
8696 
8754 
8812 
8869 
8927 
8985 
9042 
9100 
9i57 
9215 
9272 
9329 

9387 
9444 
95oi 
9558 
9615 
9673 
973o 
9787 
9844 
9900 

9957 
..i4 
or  71 
0128 
0184 
0241 
0298 
o354 
o4n 
0467 
o524 
o58o 
o636 
0693 


73o5 
7364 
7423 
7482 
754o 

7599 
7658 
7716 

7775 
7833 
7892 
795o 
8009 
8067 
8i25 
8i83 
8242 
83oo 
8358 
84i6 
8474 
8532 
85go 
8648 
8706 
8763 
8821 
8879 
8937 
8994 
9002 
9109 
9167 
9224 
9282 
9339 
9396 


73i5 
7374 
7433 
7491 
755o 
7609 
7667 
7726 
7785 
7843 
7902 
7960 
8018 
8077 
8i35 
8193 
825i 
8309 
8368 
8426 
8484 
8542 


7325 
7384 
7442 
75oi 
756o 
7619 
7677 
7736 
7794 
7853 
791 1 
7970 
8028 
8086 
8i45 
8203 
8261 
8319 
8377 
8435 
8493 
855i 


86oo|86o9 


8657 
87i5 
8773 
883i 


8946 
9004 
9061 
9119 
9176 
9234 


8667 
8725 
8783 
884o 


8956 
9013 
9071 
9128 
9186 
9243 


9291  9301 


9348 

9406 
9453j9463 
95n  9520 
9568:9577 
9625  9634 
9682  9692 

9739|9749 
9796;98o6 

9853J9863J9872 

99IO|99I9|9929 
9967:99769986 

..24  ..33  ..43 
0080^090  0099 
cff37|oi47  oi56 

0194  0203  02l3 

0250,026010269 


9358 
94i5 
9473 
953o 
9587 
9644 
9701 
9758 
98i5 


0326 
o382 


o3o7io3i7 
o364Jo373 
o42ojo43o'o439 
0477  o486  0495 
o533!o542!o552 
0589  0599  0608 
o646Jo655  o665 
0702  071 1  0721 


50 

58 

57 
56 
55 
54 
53 

52 

5 1 
5o 

49 

48 

47 
46 
45 
44 
43 
42 

4i 

4o 
39 
38 

37 
36 
35 
34 
33 
3a 
3r 
3o 
29 
28 
27 
26 

25 

24 

2  3 
22 
21 
20 

r9 

ib 

J7 
16 
i5 

1 4 
i3 

12 


60' 


20"  I  10" 


I  50" 


30"  I  20"  I  10" 


Co-sine  of  25  Degrees. 


Co-sine  of  24  Degrees. 


p  v       U"    2"    3"    4"    5"    6"    7"    8"    9" 
I,lalI>    123456789 


e   yi    011     3// 

P.  Part  J  \     ~2     \ 


5"    6"    7"    8" 
5      6      7      S 


LOGARITHMIC     TaNGKATS. 


89 


Tangent  of  64  Degrees. 


10"       20" 


40"   |   50"   | 


Tangent  of  00  Degrees. 


10"       30"       30"   1   40"   |    SO" 


IO.311S1SI1872J1925 
2l39  2192  2246 


246o;2:i3 


2334 
3i55 

3477 
3798 


22 

23 

124 
25 
2(3 

27 
2^ 
29 
3o 
3; 
32 

33 

34 
35 
36 

37 

38 

3, 

Jo 

4 1 
42 
4 'I 
4(4 
45 
46 
47 
48 

49 
5o 
5 1 

r,2 

53 
54 
55 


2781 
3 1 02 
3423 
374\ 
4o66j4i2o 
4388444s 
4710  4764 
io.3i5o32  5o86 
535454o8 
5676  5730 


5999 
632i 
6644 
6967 
7290 
76i3 
7937 
10.318260 
8584 


9232 


6o53 
6375 
6698 
7021 
7344 
7667 

799 » 
83i4 


2567 
2888 
3209 
353o 
3852 
4i73 
4495 
4817 
5 1 39 
546i 
5784 
6106 
6429 
6752 
7075 
7398 
7721 
8o45 
8368 


1979I2032J2085  59 
2299  2353,24o6 


86388692 
8962'9oi6 
9286  9340 


9556  9610  9664 
988o[9934!9988 

io.3202o5jo259lo3i3 
o529'o583|o637 
o854  0908  0962 
1 179  1233  1287 

io.33i5o4  i558  1612 
1829  :883  ig38 

2l54|2209  2263 

a48o  2534  2588 

2806  2860  2914 

y3i3i  3i86324o 


3457 
3783 

4no 


35i2 
3838 
4i64 


3566 

3892 

4219 

4436!449i|4545 

10.324763I48174872 

5089  5i44j5i98 

5416,5471  5525 

5743  5798  5852 

6071  6i25  6180 

6398'645365o7 


2620 
2941 
3263 
3584 
3905 
4227 

4549 
4871 
5193 
55i5 
5838 
6160 


X 
2674,2727 

2995i3o48 

33i6  3370 

3637369i 

3959  4oi3 

4281  4334 

46o3  4656 

4925U978 

5247,53ooJ49 

5569  5623J48 


5891  5945 

62146268 

6483JC537  6690 

68o6  686o|69i3 
7129171 83j7236 


7452 
7775 
8099 


7506,7560 

7829  7883 
8i5382o6 
8422I84768530 
874688008854 
9070  9124:9178 
9394  9448  o5o2 

97189772^826 

.  .42  .  .961.151 
0367  0421  0475 
0692  0746  0800 

IOl6  IO7I  1125 

i34i  i396!i45o 
1666  1721,1775 

1992  2046|2I00 

2317  2371  2426 
2643]2697J275i 
3023,3077 
3294 
3620 
3947 
4273 
4599 
4926 
5253 
558o 
59o7 
6234 
6562 


334934o3 
36753729 
4ooi  4o55 
43274382 
4654U708 
4981  |5o35 
5307,5362 
5634j5689 
5962  6016 
6289(6343 
6616,6671 
6944,6999 
7217I72727326 
7545j76oo!7654 
7S73  7928,7982 


6889 


672667806835 
7053(7108,7162 
7381  74367490 
770977647818 
10.328037  8092^ i47|82oi!8256'83 1 1 
8365842o|S475  853o'8584  8639 
86948749  88o3  8858J89i  3  8968 
9023  90779132  9187  9242  9297 
935ij94o6;946i  95169571  9625 
963o[9735  9790  9845,9900  9955 
56  io.33ooo9'oo64'oi  19  01740229  0284 
'  O339|o394|o44so5o3o558o6i3 
o668!o723  07780833  0888  0943 


P.  Part 


Co-tangent  of  25  Degrees. 

~VrT>"~~7~"~ 8'  ' 
27    33    38    43 


,33i327Ji382 
1657 1712 
1987  2042 
23182373 
26482703 
2979  3o34 


3309 
364o 
397i 
43o2 

10.334634 
4965 
5297 
5629 
5961 
6293 
6625 
6958 
7291 
7624 

10.337957 
8290 
8623 
8957 


3364 
3695 
4026 
4358 
4689 

5o2I 

5352 
5684 
6016 


i437 
1767 
2097 
2428 
2758 
3089 
3420 
375i 
4082 
44i3 
4744 
5076 
5408 
5740 
C072 


1492  1547  1602 
182211877  1932 


2i53 
2483 
28i3 
3i44 
3475 
38o6 
4i37 
4468 
48oo 
5i3i 
5463 
5795 


2208  2263 


a538  2593 
28682924 
3199  3254!54 
353o358553 
386i  39i6|5 


4192  4247 


4523  4579160 


4855|49io 
5i86  5242 


63491 64o4 
6681J6736 
7013,7069 
7346  7402 
7679(7735 


55i85574 
585o  5906 
6127J61826238 
6459  65i5  6670 
6792(6847  6903 
712417180  7235 
745775i37568 


5i 


7790  7846,7901  40 


8012  8068  8123  8179  8234  39 
8345  84oi  8456  85i28568  38 
8679  8734  8790  8845  8901  37 
90i2'9o68  9123  917919235  36 


9290  9346  9402,9457 


9624  9680 
9958  .  .14 

10.340292  o348 
0S27  0682 
0961  1017 

10.341206  i35s 


9735J9791 
. .70  .  ia5 
o4o4  o46o 
0738  0794 


i63i 
1966 
23oi 
2636 
2972 
33o8 
3644 
3980 


1073 

i4o8 


1687  1742 
2022  2078 

2357  24l3 


3028  3o84 
3364 3420 
3700,3756 
4o36  4092 


1 1 29 
i463 
1798 
2i33 
2469 


95i3  9569 
984719902 
.181  .237 
o5i5  0571 
o85o  0905 
i:84  i24o 
1519  1575 
i854  1910 


!9 

s8 
2189  2245J27 
2525'258i  26 


2692(2748  2804  28602916:25 


3i4oi3i96  325: 
3476  3532  3588  2"; 

38i2  3868  3924 
4i48  4204^260 


43i6  4372  4428  4484  45404596  20 


10. 344652  U708  4764 

4989  5o45,5ioi 
532653825438 
5663  5719  5775 


4821  48774933 
5i57  5a i3  5269 
5494  555o56o6 
583i  5887.5943 


/  j//  o-/  3« 

I   6  11  1] 


6000  6o56  61 12  6168,6224  62S1 
6337  6393  6449  65o6,6562|66i8 
6674  6731  6787I6843  6899'6956 
7012  7068J125J7181  7237  7293 
7350:7406,7462  7519  7575I763 1 
7688,7744,7800  78571791 3  7969 

10.348026  8o82'8i39  8195  825i  83o8 
8364,8421,8477  8533  85908646 
8703875918815  8872  8928  8985 
9041  9098J9154J921 1  9267  9324 
938094379493955096069663 
9719  9776  9832  9889  9945  . .  .2 

io.35oo58Jou5  01  71  0228  o285o34i 
0398  o454  o5i  10567  0624,0681 
073710794  o85o  0907  0964  1  020 
1077!  1 1 34  1190  1247 '  i3o4  i36o 


p.  ['lilt 


Co-tangent  of  24  Degrees. 

(  1"    2''    3"    4"    5"  ~f»"    ¥'    s*7" 
\   R     11     17    22    28    33    39    45 


)0 

LOGARITHMIC  blNES. 

1 

Sine  ot  G6  Degrees. 

c 

Sine  of  67  Degrees: 

0"    |  10"  I  20" 

30" 

40"  |  50" 

0" 

10"^  20" 

30" 

40" 

50" 

o 

9.960730  0740(0749 

0758 

0768  O777I59 

0 

9.964026 

4o35|4o44 

4o53 

4o62 

4071 

59 

I 

0786 

0796  o8o5  0814 

o824p83358 

I 

4o8o 

4089  4098 

4io6 

4n5 

4124 

58 

2 

o843 

08520861  0871 

0880088957 

2 

4i33 

4142 

4i5i 

4i6o 

4169 

4178 

57 

3 

0899 

0908  0917 

0927 

0936  0945  56 

3 

4187 

4196 

42o5 

42i4 

4222 

423l 

56 

4 

0955 

0964 

o973 

0983 

0992 

1002  55 

4 

4240 

4249 

4258 

4267 

4276 

4285 

55 

5 

ion 

1020 

io3o 

1039 

1048 

io5854 

5 

4294 

43o3 

43n 

4320 

4329 

4338 

54 

6 

1067 

1076 

1086 

IO95 

no4 

in3  53 

6 

4347 

4356 

4365 

4374 

4383 

4392 

53 

7 

1123 

Il32 

n4i 

ii5i 

1160  1 169  52 

7 

44oo 

4409 

44iS 

4427 

4436 

4445 

52 

8 

1 1 79 

11881197 

1207 

I2i6:i225|5i 

8 

4454 

4463 

4471 

44So 

4489 

4498 

5i 

9 

1235 

1244  1253 

1263 

1272  1281 

5o 

9 

4507 

45i6 

4525 

4534 

4542 

455i 

5o 

:o 

9 ,961290 

i3oo  1309  i3 18 

1328  i337 

49 

10 

9.964560 

4569 

4578 

4587 

4596 

4604 

49 

i: 

1 346 

i356Ji365  i374 

i383  i393 

48 

11 

46i3 

4622 

463i 

464o 

4649 

4658 

48 

12 

l402 

i4n]i42i  i43o 

i439i448 

47 

12 

4666 

4675 

4684 

4693 

4702 

4711 

47 

i3 

i458 

1467  1476  i485 

i495i5o4 

46 

i3 

4720 

4728 

4737 

4746 

4755 

4764 

46 

i4 

i5i3 

i523 

i532  i54i 

i55oii56o 

45 

i4 

4773 

4781 

4790 

4799 

4808 

48i7 

45 

i5 

1569 

i578 

1587  i597 

1606  i6i5 

44 

i5 

4826 

4834 

4843 

4852 

4861 

4870 

44 

16 

1624 

i634 

i643,i652 

1661  1671 

43 

16 

4879 

4887 

4896 

4905 

4914 

4923 

43 

17 

1680 

1689 

1698  1708 

1717 1726 

42 

ll 

4931 

4940 

4949 

4958 

4967 

4975 

42 

18 

i735 

1745 

175411763 

1772  1782 

4i 

18 

4984 

4993 

5oo2 

5on 

5020 

5028 

4i 

x9 

1791 

1800 

1809  1819 

i828!i837 

4o 

J9 

5o37 

5o46 

5o55 

5o64 

5072 

5o8i 

4o 

20 

5.961846 

i856 

i865|i874 

i883  1892 

39 

20 

9.965090 

5099 

5107 

5n6 

5i25 

5i34 

39 

21 

1902 

1911 

1920  1929 

1939,1948 

38 

21 

5i43 

5i5i 

5i6o 

5169 

5i78 

5i87 

38 

22 

i957 

1966  1975  1985 

1994  2003 

3? 

22 

5195 

5204 

52i3 

5222 

523o 

5239 

37 

23 

2012 

202I|2o3l  2040 

2o49j2o58 

36 

23 

5248 

5257 

5266 

5274 

5283 

5292 

36 

24 

2067 

2077  2086  2095 

2Io4,2Il3 

35 

24 

53oi 

5309 

53i8 

5327 

5336 

5344 

35 

2f 

2123 

2132  2i4i  2150J2159I2169 

34 

25 

5353 

5362 

537i 

5379 

5388 

5397 

34 

2C 

2178 

2187 

2196  2205| 221 4'2224 

33 

26 

54o6 

54i4 

5423 

5432 

544i 

5449 

33 

27 

2233 

2242 

225l  2260  2269  2279 

32 

27 

5458 

5467 

5476 

5484 

5493 

55o2 

32 

28 

2288 

2297 

23o6  23i5i2325,2334 

3i 

28 

55n 

5519 

5528 

5537 

5546 

5554 

3i 

29 

2343 

2352 

2  36 1 ,2370]  2379,2389 

3o 

29 

5563 

5572 

558o 

5589 

5598 

5607 

3o 

3c 

9.962398 

2407 

2416^425  2434!2444 

29 

3o 

9.965615 

5624 

5633 

5642 

565o 

5659 

29 

3: 

2453 

2462 

2471  2480  2489,2498 

28 

3i 

5668 

5676 

5685 

5694 

5702 

5711 

28 

32 

z5o8 

2517 

2526  2535  2544  2553 

27 

32 

5720 

5729 

5737 

5746 

5755 

5763 

27 

33 

2562 

2572 

25812590  2599  2608 

26 

33 

5772 

578i 

579o 

5798 

5807 

58i6 

26 

34 

2617 

2626 

2635  2645  2654  2663 

25 

34 

5824 

5833 

5842 

585o 

5859 

5868 

25 

35 

2672 

2681  2690  2699  270812717 

24 

35 

5876 

5885 

5894 

5902 

5911 

5920 

24 

36 

2727  2736J2745  2754J2763  2772 

23 

36 

5929  5937 

5946 

5955 

5963 

5972 

23 

37 

2781  2790 

2799  2809  2818  2827 

22 

3? 

5981  5989 

5998 

6007 

6oi5 

6024 

22 

38 

28362845 

2854  2863J2872  2881 

21 

38 

6o33  6o4i 

6o5o 

6059 

6067 

6076 

21 

39 

2890  2899 

2909  29 1 8  2927^936 

20 

39 

6o85  6093 

6102 

6111 

6119 

6128 

20 

4o 

9.962945  29S4 

2963 

2972  29812990 

X9 

4o 

9.9661366145 

6i54 

6162 

6171 

6180 

J9 

4i 

2999  3oo8 

3oi8 

3027 

3o36,3o45 

l8 

4i 

6188 

6197 

6206 

6214 

6223 

6232 

l8 

42 

3o54!3o63 

3072 

3o8i 

3090  3099 

17 

42 

6240 

6249 

6257 

6266 

6275 

6283 

J7 

43 

3io8 

3i  17 

3126 

3i35 

3i443i53 

16 

43 

6292 

63oi 

63og 

63i8 

6326 

6335 

16 

44 

3i63 

3172 

3i8i 

3i9o 

3199  3208 

1 5 

44 

6344 

6352636i 

6370 

6378 

6387 

i5 

45 

3217 

3226 

3235 

3244 

3253  3262 

i4 

45 

6395 

64o4  64i3 

6421 

643o 

6438 

U 

46 

3271 

3280 

3289 

3298 

33o733i6 

i3 

46 

6447 

64566464 

6473 

6482 

6490 

i3 

47 

3325  3334 

3343,3352 

336i 

3370 

12 

47 

6499 

6507 

65i6 

6525 

6533 

6542 

12 

48 

3379i3388 

339834073416 

3425 

11 

48 

655o 

6559 

6567 

6576 

6585 

6593 

11 

49 

3434J3443 

3452,3461  3470 

3479 

10 

49 

6602 

6610 

6619 

6628 

6636 

6645 

10 

5o 

9.5634883497 

35o6!35i5j3524 

3533 

9 

5o 

9.966653 

6662 

6670 

6679 

6688 

6696 

9 

5i 

3542  355i 

356o;3569  3578 

3587 

8 

5i 

6705 

67i3 

6722 

6730 

6739  6748 

8 

52 

3596  36o5 

36i4;3623  3632 

364i 

7 

52 

6756  6765 

6773 

6782  6790  6799 

7 

53 

365o 

3659 

3668,3677  3686 

3695 

6 

53 

6808 

6816 

6825 

6833 

6842 

685o 

6 

54 

3704 

37i3 

3722'373o  3739 

3748 

5 

54 

6859 

6867 

6876 

6884 

6893 

6902 

5 

55 

3757 

3766 

3775 

37843793 

3802 

4 

55 

6910 

6919 

6927 

6936 

6944 

6953 

4 

56 

38n 

3320 

3829 

3838^3847 

3856 

3 

56 

6961 

6970  6978 

6987 

6995 

7004 

3 

57 

3865 

3874 

3883 

3892  3901 

3910 

2 

57 

7013 

7021 

7o3o 

7o38 

7047 

7o55 

2 

58 

39i9 

3928 

3937 

3946  3g55 

3963 

1 

58 

7064 

7072 

7081 

7089  7098 

7106 

1 

59 

3972(3981 

3990 

3999  4oo8 

4017 

0 

59 

71 15 

7123 

7132 

7140  7149  7i57 

0 

eo"   |  50" 

40" 

30"  |  20" 

10" 

.5 
3 

60"    1  50" 

40" 

30"  !  20"  |  10" 

d  j 

Co-sine  of  23  Degrees. 

Co-sine  of  22  Degrees. 

2  1 

p  T,  .<  1"  2"  3"  4"  5"  6"  7"  8"  9" 
*-la$l   2   3   4   5   5   6   7   8 

p  p  A  I"   2"    3"  4"  5"  6"  7"    8"  9" 
r.iart^  j   <,   g  3   4   5   fi  ?      g 

■L , _ — _ 

Logarithmic    Tangents. 


91 


Tangent  of  66  Degrees. 


50" 


Tangent  of  67  Degrees. 


10"      20'       30"       4C        50" 


i 

c 
3 
4 

5 

e 

7 
8 

9 

i" 

1 1 
i- 
i3 
i4 
1 5 
16 

17 
18 

*9 

20 

21 
2  2 
23 

2  4 
25 
20 

^7 
28 

29 

:■;.. 

3i 

32 

33 

34 
35 
36 

3? 
38 
39 
4o 
4i 
4a 
43 
44 
4^ 
46 
47 
4^ 
49 
5o 
5i 
5a 
53 
54 
55 
56 

r>7 
58 
59 


io.35i4i7  i474 
1757 i8i4 
2097  2i54 
2438  2494 


2778 
3i  19 
346o 
38oi 
4i43 
4484 
.354826 
5i68 
55io 
5852 
6194 
6537 
6880 
7223 
7566 
7909 


835 
3:76 
3517 

3858 

4i99 
454i 
4883 

5225 

5567 
5909 

625i 
6594 


i53o 
1870 
2211 
255i 
2892 
3233 
3574 
3915 
4256 
4598 
4940 
5282 
5624 
5966 
6309 
665i 


1700  59 
2040  58 
238i  57 


1 587  i644 
927 

2267  2324 

2608  2665J2721  56 
2949  3oo5|3o62  55 
3290  3346,34o3  " 
363i  3687  3744 
3972  4029  4o86 
4427 


43134370 
4655  4712 


6937  6994 
7280  7337 
7623  7680 
7966  8024 


io.35825383io8367 
8596  8654  87i  1 
8940  8998  9055 
9284  9342  9399 
9629  9686  9743 
9973  .  .3i  ..88 

io.36o3i8o375o433 
o663  0720  0778 


4997 
5339 
568i 
6023 
6366 
6708 
7o5i 
7394 
7737 
8081 
8425 
8768 
9112 
9456 
9801 
i45 
0490 
o835 
1180 
i525 
1871 
2217 

2562 


5o54 
5396 
5738 


4769 
5iii 
5453  48 
5795 


60806137 
6423  648o 


6765 
7108 
745i 
7795 
8i38 
8482 
8826 
9170 
95i4 


2908 
3255 


ioo3  io65ii  i23 

i353  1410  1468 

361698  i756  i8i3 

2044,2I0I  2l59 

2389  2447 p5o5 
2735  2793]285i 
3o8i  3i 3y  3197 
3428  3486|3543|36oi 
3774  3832  389o  3948 
4121I4179  U237  U294 
4468J4526  4584  464i 
481514873149314989 
io.365i6a522o5a78!5336 
55io  5568,5626  5684 
5857,591 5j5973i6o3i 
6205  6263i632i  6379 
6553|G6 1 1,6669:6727 
6901  6960  7018  7076 
725o  7308  736617424 
7598  7G57i77i5l7773 
7947  8oo5  8064J8122 


2o3 

o548 
0893 
1238 
i583 
1928 
2274 
26 


6823 
7166 
75o9 
7852 
8i95 
8539 
8883 
9227 
957i 
9916 
260 
o6o5 
0950 
1295 
1641 


2966 
33i2 
3659 
4oo5 
4352 
4699 
5o46 
5394 
574i 
6089 
6437 
6785 
7i34 
7482 
783i 
8180 


2332 

>i2678 


3o24 
3370 
37i7 
4o63 
44io 
4757 
5io4 
5452 
5799 
6147 
6495 
6843 
7192 
7540  i3 
7889 
8238  11 
8529J8587  10 

9 

8 

7 
6 
5 


8296)8354  84i3  8471 

.  368645  870418762  8820  8878J8937 
89959053,9111  917092289286 
934494039461  951995789636 
96949753:9811  986999279986 

.37004410 1  o3  01 61  0219  0278  o336 
o394Jo453  o5 1 1  0569  0628  0686 
0745  o8o3  0862  0920  0978  1037 
'1095  Ii54  1212  1271  1S29  i388 
i446i5o4|i563  1621)1680  1738I 
1797  1 855  1914,1 9722031 '2090 
"  20"   lir 


ie. 372148 
2499 
285i 
32o3 
3555 
3907 
4259 
4612 
4964 
53i7 

10.375670 
6024 
6377 
673i 
7085 
7439 
7793 
8i48 
85o3 
8858 


2207 
2558 
2910 
3261 
36i3 


2265 
2617 
2968 
3320 
3672 


3965  4024 


43i8 
4670 
5o23 
5376 
5729 


4377 
4729 
5o82 
5435 
5788 


10.379213  9272 


6o83|6i42 
6436J6495 
6790  6849 
7144  7203 
749817557 
7853  7912 
82078266 
85628621 
8917  8976 


2324 

2675 
3027 

3379 

373i 
4o83 
4435 
4788 
5i4i 
5494 
5847 
6200 


2382 

2734 
3o85 
3437 


2441 
2792 
3i44 
3496 


3789,384S 


4i42 
4494 
4847 

5200 

5553 
5906 
6259 


655466i3 
690816967 
7262  7321 
7616  7675 
7971  8o3o 


9568 
9924 

10.380280 
o636 
0992 
1 348 
1705 
2061 
2418 

io.3827716 
3i33 

3491 
3849 
4207 
4565 


9627 
9983 
0339 
0695 
10S1 
1407 
1764 
2121 
2478 
2835 
3i93 
355o 
3908 
4266 
4625 


50"  1  40" 


30" 


Co-tangent  of  23  Degrees. 


33i 

9687 
..42 
0398 
0754 
mo 
1467 
1824 
2180 
538 
2895 

3252 

36io 
3968 
4326 
4684 
4923U983  5o43 
5282^342  5402 
564i  J5701  5761 
6000.6060,6120 
10. 386359,6419  6479 
6719^7796839 
707971397199 
743974997559 

7799  7859  79x9 
8159  8219/8279 
852o!858o'864o 
888o|S94i  9001 
9241I9302  9362 
9603  9663  9723 
io.389964(..24|..85 
io.39o326|o386|o446 
068807480808 
1050^1101170 
1412  1472  i533 
I775ji835  1895 
213721982258 
25oo[256r262i 
2863  2924  2985 
3227I3287I3348 


8325 
8680 
9o35 
9390 
9746 
102 
0457 
0814 
1 1 70 
i526 
i883 
2240 
2597 
2954 
33i2 
3670 


8384 
8739 
9094 
945o 
9805 
.161 


4200 
4553 
4906 
5258 
56i2 
5965 
63i8 
6672 
7026 
7380 
7734 
8089 
8444 
8799 
9i54 
9509 
9864 
.220 


0517  0576 
0873  0932 
1229  1289 
i586,i645 


1943  2002 
2299  2359 
2657|27i6 
3oi4|3o74 
3372j343i 
3729  3789 
4028I4087  Ui47 
4386  4445l45o5]a5 
4744  48o4  4864  24 

5l03|5l62  5222  23 

546i  552i|558i  22 
582o588o594oJ2i 
6180  6240,6299  20 
6539  6599:6659'  19 
16899  6959I7019  18 
!7259  7319:7379  17 
7619  767917739  16 
79798039:8099  1 5 


83998460  14 
8760882013 

9121  9181  12 

9482  9542' 1 1 

9844(9904  IO 


o5j.265 


8339 
8700 
9061 
9422 
9783 
.145 

o5o7  0567  0627 
0869,0929  0989 
ji23i  1291:1352 
'  1 593(  1  G54i  1 714 
[1956  2016  2077 
2  3 1 9  2379  244o 

'2682|2742|28o3 

|3o45,3io6  3i66 
'34093469  353o 


60" 


Co-tangent  of  22  Dejrrces. 


■-:  s 
7. 


V    I'ait 


1"    2"    3"     4"    5"    6"    7"    8"    9" 
6      12     17    23    29    35     10    4fi    :>1 


,,    .(  1"    2"    3"    4"    .V    6"    7"    8"    9" 
1!,rI$   6     12    18    21    30    30    42    48    54 


D2 

Logarithmic  Sines. 

s 

Sine  of  68  Degrees. 

a 

i 

Sine  of  69  Degrees. 

' 

0" 

10"  |  20"  1  30"  |  40" 

50" 

0" 

10" 

20" 

30" 

40- 

50" 

o 

9.9C7166 

7174I7183  7191  7200 

7208 

59 

0 

9  970152 

0160 

0168 

0176 

0184 

0192 

59 

I 

7217 

7225  7234  7242j725 1 

7259 

58 

1 

0200 

0208 

0216 

022^ 

0233 

024l 

58 

2 

7268 

7276  7285  7293 ,7302 

73lO 

57 

2 

0249 

0257 

0265 

0273 

0281 

0289 

57 

3 

73i9 

7327  7336  7344  7353 

736i 

56 

3 

0297 

o3o5 

o3i3 

o32i 

0329 

o337 

56 

4 

737o 

737873877395 

74o4 

7412 

55 

4 

o345 

o353 

o36i 

037c 

0378 

o3«6 

53 

5 

7421 

7429  74377446 

7454 

7463 

54 

5 

0394 

0402 

o4io 

0418 

0426 

o434 

54 

0 

7471 

748o 

7488  7497 

75o5 

75i4 

53 

6 

o44^ 

o45o 

o458 

o466 

0474 

0482 

53 

7 

7522 

753i 

7539  7547 

7556 

7564 

52 

7 

0490 

0498 

o5o6 

o5il 

o522 

o53o 

5a 

8 

7573 

758i 

7590*7598 

7607 

7615 

5i 

8 

o538 

o546 

o554 

o562 

0570 

0578 

5i 

9 

7624 

7632  76407649 

7657 

7666 

5o 

9 

o58G 

0594 

o6o3 

0611 

0619 

0627 

5o 

10 

9.967674 

76837691J7699 

7708 

7716 

49 

10 

9.970635 

o643 

o65i 

0659 

0667 

0675 

49 

ii 

7725 

773377427750 

7758 

7767 

48 

11 

o683 

0691 

0699 

0707 

07l5 

07?3 

48 

12 

7775 

7784  77927801 

7809 

7817 

47 

12 

0731 

o739 

0747 

0755 

0763 

0771 

4? 

i3 

7826 

783478437851 

7859 

7868 

46 

i3 

0779 

0787 

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08ll 

0819 

46 

i4 

7876 

78857893  7901 
7935  7943  7952 

7910 

7918 

45 

i4 

0827 

o835 

0842 

o85o 

o858 

0866 

45 

i5 

7927 

7960 

7969 

44 

i5 

0874 

0882 

0890 

0898 

0906 

0914 

44 

16 

7977 

7985  79948002  801 1 

8019 

43 

16 

0922 

0930 

0938 

0946 

0954 

0962 

43 

17 

8027 

8o36  8o44  8o53 

8061 

8069 

42 

17 

0970 

0978 

0986 

0994 

1002 

IOIO 

4a 

18 

8078 

808680948103 

8111 

8120 

4i 

18 

1018 

1026 

io34 

Io42 

io5o 

io58 

4i 

J9 

8128 

8i368i458i53 

8161 

8170 

4o 

x9 

1066 

1073 

1081 

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1097 

no5 

4o 

20 

9.968178 

8i87I8iq5,82o3 

8212 

8220 

39 

20 

9.971113 

1121 

1129 

n37 

n45 

n53 

39 

21 

82-28 

823782458253 

8262 

8270 

38 

21 

1161 

1 1 69 

1177 

n85 

1 193 

1200 

38 

22 

8278 

82878295,8303 
8337  83458354 

83i2 

8320 

37 

22 

1208 

1216 

1224 

1232 

1240 

1248 

37 

23 

8329 

8362 

8370 

36 

23 

1256 

1264 

1272 

1280 

1288 

1296 

36 

24 

8379 

8387'8395|84o4  84i2 

8420 

35 

=4 

i3o3  1 3i  1 

1319 

1327 

i335 

i343 

35 

25 

8429 

8437  84458454 

8462 

8470 

34 

25 

1 35 1  ]i  359 

i367 

i375 

i383 

1390 

34 

26 

8479 

8487  8495:85o3 

85i2 

852o 

33 

26 

1 398 

i4o6 

i4i4 

1422 

i43o 

i438 

33 

27 

8528 

8537  85458553 

8562 

8570 

32 

27 

1 446 

i454 

1462 

i469 

1477 

i486 

32 

28 

8578 

858785958603 

8612 

8620 

3i 

28 

1493 

i5oi 

1 509 

i5i7 

i525 

i532 

3-1 

29 

8628 

8636  8645  8653 

8661 

8670 

3o 

29 

i54o 

1 548 

i556 

1 564 

1572 

i58o 

3o 

3c 

9,968678 

868686948703 

87 1 1 

8719 

29 

3o 

9.971588 

1595 

i6o3 

1611 

1619 

1627 

29 

3 1 

8728 

873687448752 

8761 

8769 

28 

3i 

i635 

i643 

i65i 

i658 

1666 

1674 

28 

3a 

8777 

8786879418802 

8810 

8819 

27 

32 

1682 

1690 

1698 

1706 

i7i3 

1721 

27 

33 

8827 

8835  8844  8852 

8860 

8868  26 

33 

1729 

i737 

1745 

i753 

1761 

176826 

34 

8877 

8885  8893  8901 

8910 

891825 

34 

1776 

1784 

1792 

1800 

1808 

i8i5 

25 

35 

8926 

893489438951 

8959 

8967 

24 

35 

1823 

i83i 

i839 

1847 

i855 

1862 

24 

36 

8976 

8984  8992  9000 

9009  9017 

23 

36 

1870 

1878 

1886 

1894 

1902 

1909 

23 

37 

9025 

9o33  9042  9050 

9058J9066 

22 

37 

1917 

1925 

1933 

1941 

1949 

1956  22 

38 

9o75 

9083  9091 

9099 

9108  9116 

21 

38 

1964 

1972 

1980 

1988 

i995 

2003 

21 

39 

9124 

9132  9141 

9149 

9i57|9i65 

20 

39 

2011 

2019 

2027 

2o34 

2042 

2o5o 

20 

4o 

9.969173 

9182  9190 

9198 

9206  9215 

X9 

4o 

9.972058 

2066 

2073 

2081 

2089 

2097 

l9 

4i 

9223  9231  9239 

9247 

9256(9264 

18 

4i 

2105 

2112 

2120 

2128 

2i36 

2l44 

18 

42 

9272 

9280  9288 

9297 

93o5  93i3 

17 

42 

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2159 

2167 

2175 

2i83 

2190 

17 

43 

9321 

93299338 

9346 

9354  9362 

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43 

2198 

2206 

2214 

2221 

2229 

2237 

16 

44 

937o 

93799387 

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9403941 1 

i5 

44 

2245 

2253 

2260 

2268 

2276 

2284 

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9420 

9428  9436 

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9452  9461 

i4 

45 

2291 

2299 

2307 

23i5 

2322 

2330 

i4 

46 

9469  94779485 

9493 

95oi  9510 

i3 

46 

2338 

2346 

2354 

236i 

2369 

2377 

i3 

47 

95i8 

9526  9034 

9542 

955o  9559 

12 

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2385 

2392 

2400 

2408 

24l6 

2423 

12 

48 

9567 

9575  9583 

959i 

9599  9608 

11 

48 

243i 

2439 

2447 

2454 

2462 

2470 

1 1 

49 

9616 

9624  9632 

9640 

9648  9657 

10 

49 

2478 

2485 

2493 

25oi 

25oS  25i6 

10 

5o 

9 .969665 

96739681 

9689 

9697|97°5 

9 

5o 

9.972524 

2532 

2539 

2547 

25552563 

9 

5i 

9714 

9722  9730 

9738 

9746^754 

8 

5i 

2570 

2578 

2586 

2593 

2601  2609 

8 

52 

9762 

9771  9779 

9787 

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7 

52 

2617 

2624 

2632 

2640 

26482655 

7 

53 

9811 

9819  9828 

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6 

53 

2663 

2671 

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2686  2694I270I 

6 

54 

986098689876 

9884 

9893  9901 

5 

54 

2709 

2717 

2725 

2732  2740J2748 

5 

55 

99099917,9925 

9933 

9941W9 

4 

55 

2755  2763 

2771 

2778 

2786  2794 

4 

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9982  99909998 

3 

56 

2802.2809 

2817  2825 

28322840 

3 

57 

9 .9700060014  0022 

oo3o  oo38  0047 

2 

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28482855 

28632871 

28782886 

2 

58 

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0079  0087  0095 

1 

58 

2894  2901 

2909291729242932  I  j 

59 

oio3|oni'oii9oi270i36oi44 

0 

59 

2940  29472955  2963  2970  2978  0  j 

«>''    |  50"  ;  40"  |  30"  j  20"   10" 

8 

1 

1 

60"    j  50"  |  40"   30"  1  20"   10" 

C 

Co-sine  of  21  Degrees. 

Co-sine  of  20  Degrees. 

P. 

p  .  <  1"  2"  3"  4"  5"    6"    7"    8"    9"   ||  „ 
r3">  1   22345677  il  r* 

(1«  2,;  3"  4"    5"  6"  7"   8"   9" 
tarMl22   3   45   6fi7 

. ^ 

LiOGAKlTHMIC      TANGENTS. 


93 


9 

10 

1 1 

12 

i3 

i4 
i5 
r6 

■7 
18 

'9 

20 
I 
I  31 

22 

23 

24 
25 
26 

27 
28 
29 

3o 

32; 
33 
34 

35 

36 

'7 
> 
39 

4o 

4i 
4  a 

4"> 
44 
45 

4'> 

47 
4* 

49 


Tansrent  of  68  Decrees. 


.3935901365113712 
3g54  4oi5  4076 
43I84379I4440 

4683  4743;48o4 


5o47 
54i2 
5777 
6142 
6507 
6873 
.397239 
7605 
7971 
8337 


5 1 08  5169 
54735533 
5838  5898 

62o3;6264 

656816629 
69346995 
73oo  7361 

7666  7727 
80328093 


3772J3833|3894|59 
4i36l4i97  4258  58 
45oo  456i  4622  57 
4865  4926  4986  56 
5229  529o'535i  55 


rol  ? 


40"  I  50" 


8399l846o!852i  8582  8643 
87o4|8765|8826|8888|8949  9010 
9071  9132  9194  9255  9316  9377 
9438.9500  9561  9622  9683  9744 


9806  9867  9928 

.4001 73o235  0296 

o54i  0602  0664 


.400909  0971  io32  1093  1 155  1216 
1278  1S39  1 4oo  1462  1 523 ;  1 585 
i646  1 707J 1769  i83o  1892! i953 
20i5  2076;2i38i2i99'226i  2322 
2384!2445'25o7  2568!263o|269i 


5594  5655;57i6 
5959  6020^6081 
632516385,6446 
6690  6751,6812 
7o56  71 1 7  7178J50 
7422  7483,7544  49 
7788:7849  7910J48 
8i54,82i5;8276  47 
46 
45 
44 
43 
U 
4i 
4o 
39 
38 

•'7 
3.6 
35 
34 
33 

32 

3i 
3o 
29 


9989  .  .5i 
035710419  o48o 

072507870848 


2999  3o6i 
3369!343o 
3739J3800 
4109  4170 
4479J454i 
4850U911 

5220  5282  28 
5591  5653127 
5962J6024  26 


2753[23i5, 28762938 
3122,3184)3246  3307 
3492  3554!36i5  3677 
3862  3924I3985  4047 
4232  4s94  4356  44i7 

.4o46o2J4664'4726i4788 
4973  5o35: 5097  5 1 58 
5344;54o6  5468  5529 
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6086  614862 10  6272|6334:6396  25 
6458j652o|6582  6644  6706  6768  24 
6829:6891^9537015  7077  7139  23 
72oi!7263,7326|7388|745oJ75i2  22 
757417636:7698  7760  7822I7884  21 
7946:800818070  8 1 32  8 195'8257  20 

.4o83i9|838i  8443  85o5  8567!863o  19 
8692,875488168878894019003  18 
9065:9 1 279 1 89  9252  931 4]  9376  17 
9438i 950 1  9563,9625  9687  9750  16 

9812  987419937  9999  .  .6l|.I23  i  5 

.410186  o248lo3iojo373  o435  0498  i4 
o56o  06220635  o747p8o9'o872  1 3 
0934  0997, 1  o5(;  1 122  1 184  124G  12 


i3o9'i37i]i434 
1 684  1746  1809 


1496  i559 1 1 6--.  1 
18711193411996 


434  24972559262226842747 

28io[2872j2935J2997'3o6o!3i23 


5o:io.4:2o59'2i2i  2184,2246,2309  2371 
5 1 

52 

53 

54 
55 

56 

57 
58 
59 


3 1 85 

356 1 
3938 


00 


3248  33i  i  3373  3436  3499 

3624  3687  3749'33i2  3875 
4ooo'4o63,4i26,4i89l425i 
43i4  4377!444o|45o2'4565  4628 
4691 14754*48 1 7I4879<4942  5oo5 
5o68  5i3i  5194  5256  53ig  5382 
''445  55o8j557i]5634  5697  5760 
30"  ;  •SVr~  10" 


Co-tangent  of  21  Degrees. 


P.  Part 


2;'    3"    4"    5"    0"    7"    8"    9" 
12    10    25    31    37    43    49    56 


Tangent  of  69  Decrees. 


20" 


40"  I  SO" 


io.4i5823 
6200 
6578 


695617020 
73357398 
77*4  7777 


5886j5948 
62636326 
664i  6704 
7083 


8093 
8472 
885i 
9231 

10.419611 
9991 

10.420371 


8i56 
8535 
8914 
9294 
9674 
..54 
o435 


0752  0816 

u33 

i5i4 


1896 
2277 
2659 
3o4i 
10.42.3424 
3807 
4190 


1197 
i578 
i959 

234l 

2723 

3io5 

3488 

3870 

4253 
4573146374701 
4956j5o2o:5o84 
534o  54o4  5468 
572457885852 
6108  6172  6236 
6493  6557|662i 


7461 
?84o 
8219 
8598 
8978 
9358 
9738 
.118 
0498 
0879 
1260 
1641 
2023 
24o5 
2787 
3169 
355; 
3934 
43i7 


6011(6074  6137 
6389!e452  65i5 
6767|683o|6893 

714617209  7272 
7524  7587I7650 
7903  7966,8029 
828283458409 
866!  S7a5  8788 


9041 
9421 
9801 
181 
o562 


9104  9168 

9484,9547 
9864,9928 
.245j.3o8 
0625,0689 
094311006  1070 
i324  i387ji45i 
1705  1769  i832 

2o86l2l5o  22l4 

246825323596 

285o  2914  2978 
3233  3296  336o 


10.4 


6877 
27262 
7648 
8o33 
8419 


6941 
7327 
7712 
8097 

8483 


■/O06 

739! 

7776 


36i5 
3998 
438i 
4764 
5i48 
5532 


5916 


7070 
7455 
7840 
81628226 

854886i 


8805886989348998 


3679:3743 
4062  4126 
4445'45o9 
48284392 
5212^276 
5596,5660 
59S0  6o44 
63ooJ6364|6429 
6685  6749,68i3 

71347198 
7519^583 

7905:7969 
82908355 
86768741 
9062  9127 
944995i3 
9836  9900 
.223:. 287 
0610  0674 
0997,1062 
i385!i45o 
i773|i838 
2 itii  2226 
255o,26i5 
2939'3oo4 
3328,3393 


9384 
9771 
.i58 
o545 
0933 
1 320 


9191  9256  9320 

95789642  9707 

9965  .  .29  .  .94 
io.43o352  o4i6  o48i 

073908030868 
io.43i  127 1 191  1256 

i5i4  1579  1644,1708 

1 902 1 1  967  2032  2097 

2291  2356  2420  2485 
2680  2 744' 2809' 2874 
3o68  3i333i98:3263 
3458  3522'3587j3652  3717^782 
3847  ^912,3977  4o42 
4237  4302J4367.4432 
4627  4692J47574822 
io.435oi7  5082  5i47  5212 
5407  547315538,5603 
5798  5863:5929  5994 
6189  6254!632o  6385J645o  G5i5 
658i  6646!67ii'6776,6342  6907 
6972  703717103 JIG'S  7233  7299 
7364  74297495,7560, 7625  7691 
7756  7822  7887  7952  8018  8o83 
8149,8214  82798345  B4io8476 
854 1  8607  8672  87388803  8869 


4107,4172 
4497|4562 

4837495: 
5277  53^; 
5663  5733 
6o5(;  6124 


I   «"" 


Co-tangent  of  20  Degrees. 


5o 

5  b 

57 

56 
55 
54 
53 
5  a 
5i 
5o 

49 
48 

47 
46 
45 
44 
43 
42 
4i 
4o 

>9 
38 

>1 
36 
35 
34 
33 
3a 
3i 
3o 


.,     .  (  I"    2"    3"     1"    5"    6"    7"    8"    9"    j 
lllU)   G     13    19    26    32    39    45    51    58 


94 

I 

.OGARITHMIC  SlNES. 

A 

SB 

Sine  of  70  Degrees. 

(3 

Sine  of  7 1  Degrees. 

59 

0" 

10" 

20" 

30" 

40" 

50" 

°" 

10" 

20" 

30" 

40" 

50" 

o 

9.972986 

2992 

3ooi 

3009 

3oi6 

3024 

5o 

O 

9.975670 

5677 

5685 

5692 

5699 

5706 

i 

3o32 

3o39 

3o47 

3o55 

3062 

3070 

58 

I 

57i4 

5721 

5728 

5735 

5743 

575o 

58 

2 

3078 

3o85 

3093 

3ioi 

3io8 

3n6 

5? 

2 

5757 

5764 

5771 

5779 

5786 

5793 

57 

3 

3124 

3i3i 

3 1 39 

3i46 

3i54 

3162 

56 

3 

58oo 

58o8 

58i5 

5822 

5829 

5837  56 

4 

3169 

3i77 

3i85 

3192 

3200 

3208 

55 

4 

5844 

585i 

5858 

5865 

5873 

588o 

55 

5 

32i5 

3223 

323o 

3238 

3246 

3253 

54 

5 

5887 

5894 

5901 

5909 

5916 

5923 

54 

6 

3261 

3269 

3276 

3284 

3291 

3299 

53 

0 

5930 

5938 

5945(5952 

5959 

5966 

53 

7 

3307 

33i4 

3322 

333o 

3337 

3345 

52 

7 

5974 

598i 

5988  5995 

6002 

6010 

52 

8 

3352 

336o 

3368 

3375 

3383 

3390 

5i 

8 

6017 

6024 

6o3i  6o38 

6o46 

6o53 

5i 

9 

3398 

34o6 

34i3 

3421 

3428J3436 

5o 

9 

6060 

6067 

6074,6081 

6089 

6096 

5o 

IO 

9.973444 

345i 

3459 

3466 

34743482 

49 

10 

9.976103 

6110 

6117  6i25 

6i32 

6139 

49 

ii 

3489 

3497 

35o4 

35i2 

35i9  3527 

43 

11 

6i46 

6i53 

6160  6168 

6i75 

6182 

48 

12 

3535 

3542 

355o 

3557 

3565 

3572 

47 

12 

6189 

6196 

6203 

6211 

6218 

6225 

47 

i3 

358o 

3588 

35g5 

36o3 

36io 

36i8 

46 

i3 

6232 

6239 

6246 

6254 

6261 

6268 

46 

i4 

3625 

3633 

364i 

3648 

3656 

3663 

45 

i4 

6275 

6282 

6289 

6296 

63o4 

63n 

45 

i5 

367i 

3678 

3686 

3694 

3701 

3709 

44 

i5 

63i8 

6325 

6332 

633g 

6347 

6354 

44 

16 

37i6 

3724 

373i 

3739 

3746 

3754 

43 

16 

636i 

6368 

6375 

6382 

6389 

6396 

43 

*7 

3761 

3769 

37773784 

3792 

3799 

42 

J7 

64o4 

64n 

64i8 

64256432 

6439 

42 

18 

38o7 

38i4 

3822,3829 

3837 

3844 

4i 

18 

6446 

6454 

646 1 

64686475 

6482 

4 1 

x9 

3852 

385g 

3867J3875 

3882 

3890 

4o 

J9 

6489 

6496 

65o3 

65io65i8 

6525 

4o 

20 

9,973897 

3905 

3912  3920 

3927 

3935 

39 

20 

9.976532 

6539 

6546 

6553656o 

6567 

39 

21 

3942 

3950 

39573965 

3972 

3980 

38 

21 

6574 

6582 

6589 

6596  66o3 

6610 

38 

22 

3987 

3995 

4o02  4oi.O 

4017  4025 

37 

22 

6617 

6624 

663i 

6638  6646  6653 

37 

23 

4o32  4o4o 

4047  4o55 

4062  4070 

36 

23 

6660 

6667 

6674 

6681  6688 

6695 

36 

24 

4077  4o85 

4092^100 

4107U115 

35 

24 

6702 

6709 

6716 

6723  6731 

6738 

35 

25 

4l22  4l3o 

4137U145 

4i52  4160 

34 

25 

6745 

6752 

6759 

6766  6773  6780 

34 

26 

4167 

4i75 

4i82l4i9o 

4197 

42o5 

33 

26 

6787 

6794 

6801 

68o868i5 

6823 

33 

27 

4212 

4220 

42274235 

4242 

425o 

32 

27 

683o 

6837 

6844 

685i|6858  686f 

32 

28 

4257 

4264 

4272,4279 

4287 

4294 

3i 

28 

6872 

6879 

6886 

689316900 

6907 

3i 

29 

43o2 

4309 

43174324 

43324339 

3o 

29 

6914 

6921 

6928 

69356942 

6950 

3o 

3o 

9.974347 

4354 

436i4369  4370;4384 

29 

3o 

9.976957 

6964 

6971 

69786985 

6992 

29 

3: 

4391 

4399 

44o6  44i4 

4421 

4428 

^3 

3i 

6999 

7006 

7013 

7020 

7027 

7034 

28 

32 

4436 

4443 

445 1  4458 

4466 

4473 

27 

32 

7041 

7048 

7o55 

7062 

7069 

7076 

27 

33 

448i 

4488 

4495  45o3 

45io 

45 1 8 

26 

33 

7083 

7090 

7097 

7104 

7111 

7118 

26 

34 

4525 

4533 

454o'4547 

4555 

4562 

25 

34 

7125 

7i32  7i3g 

7146 

7i53 

7160 

25 

35 

4570 

4577 

45854592 

4599 

4607 

24 

35 

7167 

7174 

7181 

7188 

7195 

7202 

24 

36 

46i4 

4622 

4629  4636 

4644  465i 

23 

36 

7209 

7216 

7223 

7230 

7237 

7244  23 

37 

4659 

4666 

46744681 

46884696 
4733  4740 

2  2 

3? 

725i 

7258 

7265 

7272 

7279 

7286  22 

38 

4703 

4711 

47184725 

21 

38 

7293 

7300 

7307  73 14 

7321 

732821 

39 

4748 

4755 

4762  477° 

4777 

4784 

20 

39 

7335 

7342 

7349 

7356 

7363 

7370  20 

4o 

9.974792 

4799 

48o7'48i4 

4821 

4829 

x9 

4o 

9.977377 

7384 

73vi 

7398 

74o5 

7412 

J9 

4i 

4836 

4844 

485i 

4858 

4866 

4873 

18 

4i 

7419 

7426 

7433 

744o 

7447 

7454 

18 

42 

488o 

4888 

4895 

4903  4910  4917 

17 

42 

746i 

7468 

7475 

7482 

7489 

7496 

17 

43 

4925 

4932 

4939 

4947495414961 

16 

43 

75o3 

75io 

7517 

7524 

753o 

7537 

16 

44 

4969 

4976 

4984 

4991  4998  5oo6 

i5 

44 

7544 

755i 

7558 

7565  7572 

7579, 

i5 

45 

5oi3 

5O20 

5o28 

5o35;5o42  5o5o 

i4 

45 

7586 

7593 

7600 

7607  7614 

7621 

i4 

46 

5o57 

5o64 

5072  5079  5o86  5094 

i3 

46 

7628 

7635 

7642 

76487655 

7662 

i3 

47 

5ioi 

5io8 

5i  16  5i23|5i3o 

5i38 

12 

47 

7669 

7676 

7683 

769017697 

7704 

12 

48 

5i45 

5i52 

516015167  5174 

5182 

11 

48 

7711 

7718 

7725 

77327739 

7745 

11 

49 

5189  5196 

5204  52II  52l8 

5226 

10 

49 

7752 

7759  7766 

7773  7780 

7787 

10 

5o 

9.975233  524o  5248  5255  5262 

5270 

9 

5o 

9.977794 

7801  7808 

7815  7821 

7828 

9 

5i 

5277 

5284  5292  5299  5 3o6 

53i3 

8 

5i 

7835 

78427849 

78567863 

7870 

8 

52 

532i 

5328  5335  5343  535o 

5357 

7 

52 

7877 

78847890 

7897  7904 

7911 

7 

53 

5365 

5372  5379'5386  5394 

54oi 

6 

53 

•  79l8 

79257932 

79397946 

7952 

6 

54 

54o8 

54i6 

5423 

543o5437 

5445 

5 

54 

7959 

79667973 

7980,7987 

7994 

5 

55 

5452 

5409 

5467 

5474!548i 

5488 

4 

55 

8001 

8007J8014 

8021  8028 

8o35 

4 

^  56 

5496  55o3 

55io 

55iS;5525 

5532 

3 

56 

8042 

8o49'8o56i8o62;8o69  8076 

3 

57 

5539  5547 

5554 

556i!5568 

5576 

2 

57 

8o83  8o9o!8o97|8io4'8i  io|8i  17 

2 

53 

5583  5590 

5598 

56o556i2 

5619 

1 

58 

8124 

8i3i  8i38;8i45  8i52  8i58 

1 

59 

5627j5634 

564i 

5648  5656  5663 

0 

59 

8i65 

8i72;8i79;8i86  8193J8199 

0 

60"    |  50" 

40" 

30"  |  20"  |  10"  | 

c 

60" 

50"  |  40"  |  30"  j  20"  |  10" 

Co-sine  of  19  Degrees. 

Co-sine  of  18  Degrees. 

P. 

C  1"  0"    3"  4"  5"  G"  7"  8"  9"  1 
lail\   1   1   2   3   4   4   5   6   7 

p  p  .<  1'-'  2"  3"  4''  5"  C"  7"    8"  9" 
j  lart^  x   1   2   3   4   4   5   6   fi 

Logarithmic    Tangents. 


95 


Tangent  of  70  Degrees. 


10"   I   20"   1  30"    I   40"   I   50" 


Tangent  of  7 1  Degrees. 


30" 


80 


.438934;9000 
932719393 


9721 

•44oi 1 5 

0509 

0903 


1297 
1692 
2087 
£483 

.442879 
3275 
3671 
4067 
4464 
4861 
5259 
5656 
6o54 
6452 

.44685i 
725o 
7649 
8o48 


9786 
0180 
0574 
0969 


10 


39 
3o|io 

3i 

32 

33 
34 
35 
36 

37 

38 
39 
4o 

4 1 

4  a 
43 
44 

4r. 
46 
47 

48 

49 

5o 

5i 

53 
54 
55 
56 

57 

r>- 

5  9 


1 363 

i758 
2i53 
2549 
2945 
334i 

3737 
4i33 
453o 
4927 
5325 
5722 
6120 
6519 
6917 
73i6 

77i5 

8n5  8181 
8448J85i4!858i 
8847891418981 
92489314  9381 
9648  9715  9782 

45oo49  01 16  oi83 
o45o  o5i7|o584 

45o85i  09180985 
1253  1320  1387 
j.655  1722  1789 
2o57j2i24  2191 
2460:252712594 


9065 

9458 
9802 
0246 
o64o 
io34 
1429 
1824 
2219 
26i5 
3oii 
3407 
38o3 
4200 
4596 
4994 
5391 
5789 
6187 
6585 
6984 
7383 
7782 


9i3i {9196  9262 
9524  9590  9655 
99I8J9983'  49 
o3i2  0377  o443 
070610771  0837 

IIOOII66  1232 
l495  l56ll627 
189O  I956'2022 

2285  235i  2417 
2681  2747(2813 
3i43|3209 
3539  36o5 
39354001 
4332I4398 
4729)4795 
5i26  5192 
5524j559o 
592115988 
6a53J632o6386 
665267186784 
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2208  2276  2345 


7516,7582 
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4261  4329U398 

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6321I6390  64596528 

6734  68o3'6872!694i 
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4o55 
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4124 
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9272  9342  94i3  9483  9554  9624120 


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24i3  248i  255o 
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42 

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44 
45 
46 

47 

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53 
54 
55 
56 
57 
58 
59 


10.479695J9765  9836,990619977  .  .47 

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o542  0612  o683  0754  0824  0895 

0966  1  o36i  1 1 07  1 1 78  1248  1 3 19 


1390  1 46 1  1 53 1  1602  1673 
1814  i885  1956  2027  2098 

2239  23l0  238l  2452  2523 

2665  2736. 2807I2877  2948 
30903161323213303 


3729 

4i56 
4583 
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3374 
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1744 
2169 
2594 
3019 
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42274298 
4654  47^5 
5o8i  5i  5a 


35i6  3587|3658 
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5223  5295  5366J5437  55o6 
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7365  7436,75o8  75807651  7*»a3J 
7794  7866  7937  8009J8081  *■: :  52| 


Co-tangent  of  1 9  Degrees. 


Co-taiiirent  of  18  Decrees. 


II 


P  Part  J  *"    K    3"    4"    :'"    ,;"    7"    8" 
{■7      J3    20    27    ;)3     10     17    54 


P  Part  J  l"    2"    3''    4"    5"    fi" 


7"    8"    9" 
49    5f    6J 


96 


Logarithmic   Sines. 


.a' 

3 

Sine  of  72  Degrees. 

2 

Sine  of  73  Degrees. 

0" 

10"  I  20"  |  30"  |  40" 

50" 

0"    1  10" 

20'' 

30" 

40" 

50" 

o 

9.978206 

821 3 J8220  8227.8234 

824l 

59 

O 

9.980596(0603 

0609 

0616 

0622 

0628 

59 

I 

8247 

82548261  8268,8275 

8282  58 

I 

o635 

o64i 

o648 

o654 

0661 

0667 

58 

2 

8288 

8295 

83o2  83o9'83i6 

8322 

57 

2 

o673 

0680 

0686 

0693 

0699 

0706 

57 

3 

8329 

8336  8343;835o'8357 

8363 

56 

3 

0712 

0718 

0725 

0731 

o738 

0744 

56 

4 

837o83778384!839i  8397 

84o4 

55 

4 

0750 

0757 

0763 

0770 

0776 

o783 

55 

5 

84n84i8  8425  843i  8438 

8445 

54 

5 

0789 

o795 

0802 

0808  o8i5 

0821 

54 

6 

8452  84598465(8472  8479 

8486 

53 

6 

0827 

o834 

0840 

0847  o853 

0859 

53 

7 

849318499  85o685i3852o 

8527 

52 

7 

0866 

0872 

0878 

o885 

0891 

0898 

53 

8 

8533  854o  8547  8554  856i 

8567 

5i 

8 

0904 

0910 

0917 

0923 

0930 

0936 

5i 

9 

8574 

858i  8588  8594  8601 

8608 

5o 

9 

0942 

0949 

0955 

0961 

0968 

0974 

5o 

IO 

9.978615 

8622862886358642 

8649 

49 

IO 

9.980981 

0987 

0993 

1000 

1006 

1012 

49 

II 

8655 

86621866986768682 

8689 

48 

11 

1019 

1025 

io3i 

io38 

1044 

io5i 

48 

12 

8696 

87038709,87168723 

8730 

47 

12 

1057 

io63 

1070 

1076 

1082 

1089 

47 

i3 

8737 

8743875087578764 

8770 

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i3 

1095 

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1 108 

ni4 

II20 

1127 

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8784:8791  87978804 

8811 

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14 

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1139 

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1 1 58 

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8817 

8824  883i'8838  8844 

885i 

44 

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1 171 

1177 

1184 

1190 

1196 

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44 

16 

8858 

8865:8871  8878  8885 

8892 

43 

16 

1209 

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1222 

1228 

1234 

1241 

43 

17 

8898 

89058912  8918,8925 

8932 

42 

17 

1247 

1253 

1260 

1266 

1272 

1279 

42 

18 

8939 

8945  8952'8959  8965 

8972 

4i 

18 

i-?85 

1291 

1298 

i3o4 

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i3i7 

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8979 

8986  8992  8999 

9006 

9012 

4o 

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i323 

1329 

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i342 

1 348 

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20 

9.979019 

9026  9033  9039 

9046 

9o53 

39 

20 

9.981361 

1367 

1373 

i38o 

i386 

1392 

39 

21 

9059 

90669073  9079 

9086,9093 

38 

21 

i399 

i4o5 

i4n 

i4i7 

i424 

i43o 

38 

22 

9100 

9106-91 13,9120 

9126,9133 

37 

22 

i436 

i443 

1449 

1455 

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i468 

37 

23 

9140 

9146  9i53  9160 

9166 

9i73 

36 

23 

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i48o 

1487 

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1499 

i5o5 

36 

24 

9180 

9186  9193^200 

9206 

9213 

35 

24 

l5l2 

i5i8 

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i53i 

i537 

1 543 

35 

25 

9220 

9227  9233  9240 

9247 

9253 

34 

25 

1 549 

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i562 

i568 

i574 

i58i 

34 

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9260 

9207  927319280 

9287 

9293 

33 

26 

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i593 

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1606 

1612 

1618 

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1  27 

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9326 

9333 

32 

27 

1625 

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i637 

1 643 

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i656 

32 

28 

9340 

9346935319360 

g366 

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28 

1662 

1668 

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1681 

1687 

1693 

3i 

29 

9380 

9386  939319400 

9406  94i3 

3o 

29 

1700 

1706 

1712 

1718 

1724 

i73i 

3o 

3o 

9.979420 

9426  9433  9439 

94469453 

29 

3o 

9.981737 

1743 

1749 

i756 

1762 

1768 

29 

3i 

9459 

9466  9473  9479 

9486  9492 

28 

3i 

i774 

1781 

1787 

i793 

1799 

1806 

28 

32 

9499 

95o6  9512  9519 

9526  9532 

27 

32 

1812 

1818 

1824 

i83o 

1837 

i843 

27 

33 

9539 

9545  9552  9559 

9565  9572 

26 

33 

1849 

i855 

1861 

1868 

1874 

1880 

26 

34 

9579 

9585  9592  9598 

9605  9612 

25 

34 

1886 

i893 

1899 

1905 

1911 

1917 

25 

35 

9618 

9625  9631  9638 

9645|965i 

24 

35 

1924 

1930 

1936 

1942 

1948 

1955 

24 

36 

9658 

9664  9671  9678 

9684  9691 

23 

36 

1961 

1967 

i973 

1979  19S6 

1992 

23 

37 

9697 

9704  9711  9717 

9724  9730 

22 

37 

1998 

2004 

2010 

20l6  2023 

2029 

22 

38 

9737 

974397509757 

97639770 

21 

38 

2o35 

204l 

2047 

2o54 

2060 

2066 

21 

39 

9776 

978397909796 

9803:9809 

20 

39 

2072 

2078 

2084 

209I 

2097 

2io3 

20 

4o 

9.979816 

9822  9829  9836  9842'9849 

r9 

4o 

9.982109 

2Il5 

2122 

2128 

2l34 

2l4o 

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4i 

9855 

9862986898759881  9888 

l8 

4i 

2i46 

2l52 

2159 

2i65 

2171 

2177 

l8 

42 

9895 

9901  9908,9914 

9921,9927 

ll 

42 

2i83 

2189 

2195 

2202 

2208 

22l4 

17 

S,3 

9934 

99409947,9954 

9960  9967 

16 

43 

2220 

2226 

2232 

2239 

2245 

225l 

16 

44 

9973 

9980  9986  9993 

9999  ...6 

i5 

44 

2257 

2263 

2269 

2275 

2282 

2288 

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45 

9.980012 

0019  0026|0032 

0039  oo45 

i4 

45 

2294 

23oo 

23o6 

23l2 

23i8 

2324 

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oo52 

oo58  oo65  0071 

0078  0084 

i3 

46 

233i 

2337 

2343 

2349 

2355 

236i 

i3 

47 

0091 

0097  oio4  OIIO 

0117,0123 

12 

47 

2367 

2373 

238o 

2386 

2392 

2398 

12 

48 

oi3o 

oi36  oi43  0149 

oi56  oi63 

11 

48 

24o4 

2410 

2416 

2422 

2429 

2435 

11 

49 

0169 

0176  0182  0189 

0195  0202 

IO 

49 

244l 

2447 

2453 

2459 

2465 

2471 

10 

5<i 

9.980208 

02i5  0221  0228 

0234  0241 

9 

5o 

9.982477 

2484 

2490 

2496 

2502 

25o8 

9 

5i 

0247 

0254  0260  0267 

0273  0280 

8 

5i 

e5i4 

2520 

2526 

2532 

2538 

2544 

3 

O2 

0286 

0293  0299'o3o6 

o3i2  o3i8 

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52 

255i 

2557 

2563 

2569 

2575 

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7 

53 

o325 

o33ilo338io344 

o35i  o357 

6 

53 

a587 

25o3 

2599 

2605 

2611 

2617 

6 

54 

o364 

0370  0377  o383 

0390  0396 

5 

54 

2624  263o 

2636 

2642 

2648 

2654 

5 

55 

o4o3 

0409  o4i6  0422 

0429  o435 

4 

55 

2660  2666 

2672 

2678 

2684 

2690 

4 

56 

0442 

o448o454o46i 

0467  o4?4 

3 

56 

2696,2702 

2709*2715 

2721  2727 

3 

57 

o48o 

04870493,0500 

o5o6  o5i3 

2 

57 

2733,2739 

2745,275112757  2763 

2 

58 

0519 

o525  o532  o538 

o545  o55i  1 

58 

27692775  2781  2787 

2793^799 

1 

59 

o558 

o564,o57ijo577  o583  0590  0 

59 

28o5:28n!28i7!2824 

283o  2836  0 

60" 

50"  |  40"  |  30"  |  20"   10"  | 

«  i 

1 

60"    )  50"  j  40"   30"  |  20"   10"  i  .. 

Co-sine  of  17  Degrees. 

2  II 

Co-sine  of  16  Degrees. 

l§ 

r. 

p   5  1"  2"  3"  4"  5"  6"  7"    8"  9" 
"in\   1.1   333   4558 

P. 

T,   (1"  2"  3"  4"  5"  6"  T' 
lart\    l   l   o   2   3   4   4 

5 

(  i 

Logarithmic    Tangents. 


97 


Tangent  of  72  Degrees. 


10"  |  20"  |  30"  I  40'  I  50" 


Tangent  of  73  Degrees. 


10"  I  20"   30"   40" 


50" 


o 
I 

a 
3 
4 
5 
6 

7 
8 

9 
to 

1 1 

19 

i3 

1 4 

1 5 
16 

J? 
18 

19 

30 

21 
22 
a3 
24 
a  5 
26 

-7 
28 
39 
3o 
3i 
3a 
33 
34 
35 
36 

37 
38 
39 

4o 
4i 
4a 

4:: 
44 
4r- 
46 

47 
48 

49 

!  5o 
|5i 

,5a 
3 

i54 
55 

56 

57 
I  58 

59 


10.488224 
8654 
9084 
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10.490378 
0809 
1241 


8296I8367 
872618797 
91 56  9228 
9587  9659 
18!.  .90 


0449 
1 
i3i3 


1674  1746 

2107.2179 

10.492540  2612 


2973 
3407 
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4276 
4711 
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5582 
6018 
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10.496891 
7328 
7765 
8203 
864i 


3o46 
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39i4 
4348 
4783 
5219 
5654 
6090 
6527 
6964 
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7838 
8276 
87i4 


o52I 

0953 
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1818 

225l 

2684 
3n8 
3552 
3986 
4421 
4856 
5291 
5727 
6i63 
6600 


8439 


9300 
973i 
.  162 
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1025 

i458 
1890 

2323 

757 
3190 

3624 
4059 

4493 
4928 
5364 
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85n  8582 
8941.9013 
9371  9443 
9802  9874 
234  .  3o6 
o665  0737 


1097 
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1962 
2395 
2829 
3263 
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4i3i 
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1 1 69 
1602 
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2468 
2901 
3335 
3769 
4204 
4638  45 
44 


5ooi:5o74 
5437J5509 
5872  5945 


6236  63o9J638i 
6672 


7036J7109 


674568i8 


7474 
7911 

8349 

8787 


9080,915319226 


9519)9592 

9958  L.3i 
10.500397  0471 

0837 0911 
10  5oi278|i35i 

1718 

2159 

2601 

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3485 

3927 

4370 

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5257 
10. 505701 


1792 

2233 

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614616220 
6590  6664 
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748i 


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3190 
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9299 

9738 
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0617 
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2822 
3264 
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5479 
5923 
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68 1 3 
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7182 
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9372 
9811 
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1 571 
2012 
2454 
2895 
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4223 


7255 
6792 

8i3o 
8568 
9007 
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7110  7184 
7555  7630 
7927  8001  8076 
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8820  8894I8969 
9267  9341  9416 
9714197899863 
10  510162  0237  o3n 
0610  o685  0760 
1059  1  r  34  1208 
i5o><ii5S2|iG57 

I957  2032  2IO7 

2407)2482)2557 
2857  2932)3007(3082 
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375*  3833  3908  3984 

4209  4285;436oj4435 


.324 

0764 

1204 
1645 
2086 
2527 
2969 

34n 
3854 
96 


4666i474o 
5109  5i83 
5553  5627 
5997  6071 
6442,65i6 
68876961 
7332  7407 
7778,7853 
8224,8299^4 
867i!s745;i3 


9043.91 1819192  12 


9490 
9938 
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9565,9640]  1 1 
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0461  o535  9 
0909,0984  8 

ia83|i358  1433  7 
1732  1807J1882!  6 

2l82  2257  2332 

2632  2707 
3i57 
36o8 
4059 
45io 


50"  1  40"   :«o" 


2-S2 
3a32 
3683 
4 1 34 
1586 
"10" 


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5n3 
5565 
6018 
6471 
6925 
7379 
7833 
8288 
8743 

,5 19 1 99 
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I0.520II I 


4736j48i2J4887|4962|5o38 
5i88|5a64!5339  54i5  5490 


564i 
6094 
6547 
7001 


57i6 
6169 
6623 
7076 


7455l753o 
7909I7985 
8364  844o 


5792  5867  5943 
6245  63206396 

6698  677416849 
7152J722817303 
7606  7682  7758 
8061  8137821s 
851685928667 


8819:8895,8971  9047  9133 
9275:9351  942719503  9579 


9731  9807  9883 
018710263  o34o 
o568  0644.0720  0797 


1025  iioi  1178  ia54 
i483  1559  i635  1712 
2017  3094J2170 
2476^552  2628)2705 
3on|3o87  3i64 
36s3 
4o83 
4544 
5oo4 
5465 
592- 


1941 
2399 

2858 
33i7 
10.523777 
4237 
4697 
5i58 
5619 


9959I.  .35 
o4 1 6  0492 
0873  0949 
i33o|i4o7 
1786  1864 
2246 


3470 
3930 
4390 
485i 
53i2 
5773 


3547 
4007 
4467 
4927 
5388 
585o 
63i2 
6774 
7237 
7700 
8i63 


2323 

2781 

324l 

3700 

4i6o 

4620 

5o8i 

554a 

6oo4 

6389;6466 

685i  6928 

73147391132 

7777J7S5AJ3I 


Co-tangent  of  17  Degrees. 


L 


(    ill      nil      -til       Ail      ell 

'       J|   7      15    22    20    37 


_. 


2934 
3394 
3853 
43i3 
4774 
5235 
5696 
6o8i]6i58|6235 
654366206697 
7005  7082  7160 
7468  7545  7623 
7931  8009  8086  8i63  824:i33i8 

io.528395|8472'855o  8627  8705  8783 
885918937  9014  9091  9169  9246 
9324J9401 J9479  9556  9634I9711 
97899866)9944  •  .21  ..99J.177 

io.53o254  o332jo4o9'o487  o565|o642 
0720  0798J0875I0953  io3i  1 108 
n86ji264,i342Ji4i9  1497  1^75 
i653  1731U808  1886  1964  ao4a 
2120  2198  2276^353  243i  2509 
2587  2665  2743  2821  2899  2977 

10. 533o55j3i33|32i  1  3a89  3367  3445 
3523 13602  368o  3758,3836  3oi4 
3992^070)4149  4227  43o5  4383 
446i  454o46i8  4696J4774|4853 
4g3i  50095088  5i66  5244  53a3 
54oi  5479  5558; 5636i 57 1 5)5793 
5872  5950^6028  6107  6i85;6264 
6342  6421  6499  657816657  6735 
68i4  6892  69717050  712817207 
72857364  7443J7522  76007679 

10.53775878367915  7994  8073  81 5 1 
823o:83o9;8388  8467  854''  -<;-4 
8703^782)8861 894090  1  9  9098 
91779256,9335  94 1 4  9493  957a 
965i  97309809  9888  9967  ..46 

10.540125)0204,0283.0362044^  '"^2  1 
06000679,0758  qS "7  09170996 
1075  n 54  1234  1 3 1 3j  1 392  1472 
i55i|i63o  17m  17^9,1868^948 
2027  2106  2i86j2265  a345  a4»4 


59 
58 

'■7 
56 
j5 
54 
53 
5  a 
5i 
5o 

49 
48 

47 
46 
5 
44 
43 
42 
4i 
4o 

•9 
38 

'7 
36 

''.5 
';; 


:»•"  ;  20" 


Co-tangent  of  16  Degrees. 


9" 
66 


3o 
20 

ad 

-7 
26 

25 

24 

23 
2  2 
J  I 
20 

'9 

IN 

17 
l6 

i5 
•4- 
t3 

12 

1 1 
i" 

9 
5 

7 
B 
5 
4 
3 
3 
I 
o 


I".  Tart 


(  1"  2"  3" 
}  8   13  23 


5"  6"  7"  b"    0" 
39  4  G  54  62  70 


98 


Logarithmic    Sines. 


I0>  JP  Ft, 


6 

7 
8 

9 
io 
ii 

12 

i3 
i4 
i5 
16 

17 

i 

l9 

20 
21 
22 
23 
24 
25 
26 

27 
28 
29 

3o 
3i 

32 

33 
34 
35 
36 

37 

38 
39 
4o 
4i 
42 
43 
44 
45 
46 

47 

48 

49 
5o 
5i 

53 
54 
55 
5G 

5  7 
5s 
5o 


Sine  of  74  Degrees. 


9.982842 
2878 
2914 
2950 
2 

3022 

3o58 
3094 
3i3o 
3i66 

983202 
3238 
3273 
3309 
3345 
338i 
34i6 
3452 
3487 
3523 

983558 
3594 
3629 
3664 
3700 
3735 
3770 
38o5 
384o 
3875 
9.983911 
3946 
3981 
4oi5 
4o5o 
4o85 
4120 
4i55 
4190 
4224 

984259 
4294 
4328 
4363 
4397 
4432 
4466 
45oo 
4535 
4569 
9.984603 
4638 
4672 
4706 
474o 
4774 


10" 


20"  I  30"|  40"   50" 


2848  28542860  2866 
2884j289c(  2896,2902 


2920.2926  2932 

956.2962  2968 

2992,2998  3oo4 


2938 
2974 
3oio 


3028  3o34,3o4o  3o46 
3o64j3o7o|3o76  3o82 
3ioo!3io63ii2  3n8 
3i36|3i42|3i48  3i54 
3172  3178^184  3190 

3208  32l4,3220  3226 

3244325o  3256 
3279  3285,3291 
33i5  332i|3327 
335i|3357  3363 
398 


3434 
3469 
35o5 
354o 
3576 


3386  3392 
3422  3428 
3458^3464 
3493  3499 
3529'3535 
3564  3570 
3599  36o5J36n 
3635,3641  3647 
367036763682 
37053711  3717 
3741  3747,3752 
377637823788 
38n!38i73823 
3846  3852  3858 
3881:38873893 
3916  3922  3928 


3951  3957 
3986  3992 

4o2I  4027 

4o56  4062 
4091  4097 
4126  4i32 
4i6i  4166J4172 
4195  4201 U207 
423o  4236  4242 
4265  4270  4276 


3963 
3998 
4o33 
4o68 
4io3 
4i37 


42994305 

43344340 
43684374 
44o3  4409 
4437|4443 

44724477 
45o6  45i2 
454o|4546 
4575:458o 
4609  46i5 
4643  4649 
46774683 
47124717 
4746,4751 
478o!4785 
48o8|48i4!48i9 
4842  4848J4853 
48764882,4887 
49104916.4921 


50" 


43n 
4345 
438o 
44i4 
4449 
4483 
45i8 
4552 
4586 
4620 
4655 
4689 
4723 

4757 
4791 
4825 
4859 
4893 
4927 


3262 
3297 
3333 
3369 
34o4 
344o 
3475 
35n 
3546 
3582 
36i7 
3653 
3688 
3723 
3758 
3794 
3829 
3864 
3899 
3934 
3969 
4oo4 
4039 
4074 
4io8 


2872 
2908 
2944 
2980 
3oi6 
3o52 
3o88 

3l24 

3i6o 
3196 

3232 

3268 
33o3 
3339  46 
3375  45 
34io  44 
3446  43 
348i  42 


35i7 
3552 
3588 
3623 
3658 
3694 
3729 
3764 
3799 
3835 
3870 
3905 
3940 
3975 
4oio 
4o45 
4079 
4n4 


4i43!4i49 

4178  4i84 

4213I4218 

4247  4253 

4282U28 

4317432 

435i|4357 

43864391 

4420  4426 

4455446o 

44894495 

45234529 

45584563 

45924598 

4626  4632 

466o4666 

46944700 

47294734 

47634768 

4797  4802 

483i4836 

48654870 

4899  4904 

4932  4938 


Co-sine  of  15  Degrees. 


„  p   J  1"  2"  3"  4"  5"  6"  7"    8"  9" 
r.ran,  i   i   2   2   3   3   4   5   5 


Sine  of  75  Degrees. 


.984944 
4978 
5on 
5o45 
5o79 
5n3 
5i46 
5i8o 
52i3 
5247 

.985280 
53i4 
5347 
538i 
54 1 4 
5447 
548o 

55i4 
5547 
558o 

•9856i3 
5646 
5679 
5712 
5  745 
5778 
58n 
5843 
5876 
5909 

.985942 
5974 
6007 
6039 
6072 
6io4 
6i37 
6169 
6202 
6234 

.986266 
6299 
633i 
6363 
6395 
6427 
6459 
6491 
6523 
6555 

.986587 
6619 
665i 
6683 
6714 
6746 
6778 
6809 
684i 
6873 


10" 


4949 
4983 
5017 
5o5i 
5o84 
5n8 
5i52 
5i85 
5219 

5252 

5286 

5319 
5353 
5386 
5419 
5453 
5486 
5519 
5552 
5585 
56i8 
565i 
5684 


4955 
4980 

5o20 

5o56 
5090 
5 1 24 
5i57 
5191 
5224 
5258 
5291 
5325 
5358 
5392 
5425 
5458 
5491 
5525 
5558 
5591 
5624 
5657 
5690 


5717  5723 


5750 
5783 
58i6 
5849 
5882 
5gi4 

'947 
5980 
6012 
6o45 
6077 
6110 
6142 
6i75 
6207 
6239 
6272 
63o4 
6336 
6368 
64oi 
6433 
6465 
6497 
6529 
656i 
6593 
6624 
6656 
6688 
6720 
675i 
6783, 


5756 

5789 

5822 

5854 
5887 
5920 
5952 
5985 
6018 
6o5o 
6o83 
6u5 
6i48 
6180 
6212 
6245 
6277 
6309 
6342 
6374 
64o6 
6438 
6470 


30"   40" 


4961 
4995 
5o28 

5o62 
5096 
5129 
5i63 
5 1 97 
523o 
5264 
5297 
533o 
5364 
5397 
543o 
5464 
5497 
553o 
5563 
5596 
5629 
5662 
5695 
5728 
576i 
5794 
5827 
586o 
5893 
5925 
5958 
599i 
6023 
6o56 
6088 
6121 
6i53 
6186 
6218 
625o 
6282 
63i5 

6347 
6379 
64n 
6443 

6475 


663o 
6661 
6693 
6725 
6757 
6788 
68i5i6820 


65o2  6507 
65346539 
6566  657i 
65986603 


68466852 
68786883 


6635 
6G67 
6699 
6730 
6762 
6794 
6825 
6857 
6888 


4966 

5ooo 

5o34 

5o68 

5io 

5i35 

5169 

520 

5236 
5269 
53o3 
5336 
5369 
54o3 
5436 
5469 
55o2 
5536 
5569 
56o2 
5635 
5668 
5701 
5734 
5767 
58oo 
5832 
5865 
5898 
5931 
5963 
5996 
6029 
6061 
6094 
6126 
6159 
6191 
6223 
6256 
62S8 
632o 
6352 
6384 
6417 

6449 
648 1 
65i3 
6545 
6577 
6608 


50" 


4972 
5oo6 
5o4o 
5073 
5107 
5i4i 
5i74 
5208 
5241 
5275 
53o8 
5342 
5375 
54o8 
5442 
5475 
55o8 
554i 
5574 
5607 
564o 
5673 
5706 
5739 
5772 
58o5 
5838 
587i 
5903 
5936 
5969 
6001 
6o34 
6067 
6099 
6i32 
6164 
6196 
6229 
6261 
6293 
6325 
6358 
6390 

6422 
6454 

648G 
65i8 
655o 
6582 
66i4 
664oj6646 
6672J6677 
6704  6709 


6736 
6767 
6799 


6741 
6773 
G8o4 


683i!G836 

68626867 
6894)6899 


Co-sine  of  14  Degrees. 


59 

58 

57 
56 
55 
54 
53 
52 
5 1 
5o 

49 

48 

47 
46 
45 
44 
43 
42 
4i 
4o 

39 
38 

37 

3G 
35 
34 
33 

3'4 

3i 
3o 
29 
28 

27 
26 

25 

24 

23 
22 
21 
20 

*9 

18 

17 
16 
i5 
i4 
i3 
12 


P.  Part. 


1"    2;/    3"    4" 
112      2 


5"    6"    7"    8"    9" 
3      3      4      4      5 


LOGARITHMIC      T  A  N  G  E  N  T  S. 


99 


Tangent  of  74  Degrees. 


10"      20        30"       40"       50" 


Tangent  of  75  Degrees. 


i 

6 

7 
8 

9 
10 

ii 

12 

i3 
i4 
i5 
16 

J7 

18 

*9 

20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

3o 
3i 

32 

13 

34 

35 

36 

37  10, 

38 

39 

4o  10. 

4i 

42 

43 

44 

45 

46 

47 
48 

49 

5o  10 
5i 

5s 
53 

54 
55 

56] 
57  10 
58| 
59 


>. 5425o4  2583 
2981  3o6o 
3458i3538 
393614016 
44i4|4494 
4893U973 
5372  5452 
5852  5932 
6332  6412 


68i3 

.547294 

7775 

8257 

8740 

9223 

9706 

.550190 

0674 

1169 

1 644 

,552i3o 

2616 

3l02 


2663 
3i4o 
36i7 
4095 
4574 
5o53 
5532 
6012 
|649; 


689316973 


7454 
7936 
84i8 
8901 
9384 
9867 
o35i 
o836 

l320 

1806 

2292 


to 


7374 

7856 

8338 

8820 

93o3 

9787 

0270 

0755 

1240 

1725 

221 1 

2697*2778 

3i833265 
3589|3670J3752 
4077U158  4239 
4565J4646I4728 
5o53,5i35J52i6 
5542  5624  0705 
6o32  61 1 3J6195 
652i  6603^685 
557012  7093  7175 
75o3  7584  7666 
7994  8076  8i58 
8486  8568  865o 
8978  9060  9142 
9471  9553!9635 
9964  .  .46!.  128 
56o457  o54o  0622 
0952  io34  1 1 16 
i446!  1 529J 161 1 
561941  2024  2106 
2437I2520  2602 
2933|3oi6|3o99 
343o'35:2'3595 
3927  4010^093 
44244507*4590 
4922  5oo5!5o88 
542i|55o4'5587 
5920  6oo3  6086 
642oJ65o3'6586 
566920700'!  7086 
7420J7504I7587 
7921  800:')  8088 
8423  85o6|859o 
8925  9008  9092 
9427  o5t  1  </">(/> 
,9930*..  1 4  ..98 
570434  o5i*  0602 
0938'l022  1  m<i 

i44a[i5a7  ifii  i 

"60"    I  W   I  4()" 


2742 
3219 
3697 
4i75 
4654 
5i33 
56i2 
6092 
6572 
7o53 
7535 
8016 
3498 
8981 
9464 
9948 
o432 
0916 
i4oi 


2822  2901 
3299  3378 
3777I3856 
4255J4335 
473348i3 
52i3  5292 


5692 
6172 
6653 
7i33 
76i5 
8097 


5772 
6252 
6733 
7214 
7695 
8177 


8579865947 
9062  9142  46 
9545:9625  45 
..28  .109U4 
o5i3o593  43 
099711078142 


i373 


1482  i563 
1968:2049 
2454'2535 
2859^2940  302I 
3346|3427J35o8 
383339143995 
432i  44o2!4483 
4809  4890*4972 
5298  5379*5461 
57875868*5950 
6276  6358'644o!3i 
67666848693030 
7257  73397421  29 
7830I7912  28 
8322'84o427 
88i4!889626 
93o6|9388  25 
97999881I24 
.2931 .37523 
0787  0869I22 
1 281  x364ax 
1776  1859*20 
2272*2354*19 
2768  285o'i8 
3264!3347  17 
376i*3844  16 


7748 
8240 
8732 
9224 
9717 
.210 
0704 
1 199 
1694 
2189 
2685 
3i8i 
3678 
4i75 
4673 
5.7 


Co-tangent  of  1 
P.PartJ  l"   2"  3"  4"~ 


4258  434i 
47564839 
5255  5338 
5670I5754  5837 
6170  6253  6336 
66696753.6836 
7170  7253  7337 
7671  7754  7838 
^i72'82558339 

J8674  8757J884i 

9176  9260  9343 
9679^763  9846 
.182  .266  .35o 
^7o'o854 
1  190  1274  1  ''>~>s 

if,,/,  1779  186  I 

J  :i<v  go"~ 
■'>   Dejnrecs. 


9 
10  ic 

11 
12 
1 3 
i4 
1 5 
16 

17 
18 

'9 
20 

21 

22 

23 
25 

26 

27 
28 
29 

3o 

3i 

32 

33 
34 
35 
36 

37 

38 

39 

4o 
4 1 
4  a 
43 
44 
45 
46 

4; 
48 

49 

50  n 

5 1 

52 

53 
54  Jo 
55 
56 

58 
59 


2116I2200I2285I2369 


2706  2790  2876 


3212 
37I9 
4227 
4735 
5243 
5752 
6261 


6686,6771 


7197 
7708 
8219 
873l 
9243 

9756 
0270 
0784 
1299 
1814 
2329 


7282 
7793 
83o4 
8816 
9329 
9842 
o356 
0870 
1 384 


3297  338i 
38o4  3888 
43n  4396 


4904 
54i3 
5922 
643 1 
6941 
7452 
7963 


4819 
5328 
5837 
6346 
6856 
7367 
7878 

8390  8475 
89028987 
94i4,95oo 
9928  ..i3 
0441  0527 
0956  io4i 
1470  i556 
190011986  2072 
24i5  25oi  2587 
284612932  3oi8  3 io4 
3362  3449  3535  3621 


.57i948 

2453  2537  2622 

2959  3o44  3128 

3466  355o  3635 

3973  4o58  4i42 

448i  4565  465o 

49895o73  5i58 

5497  5582  5667 

6007  6091  6176 

65i6 
,577026 

7537 

8o48 

856o 

9073 

9585 
,580099 

06 1 3 

1127 

1642 
582i58 

2674 

3190 

3707  3793  388o 

4225  43i  1  4397 

474348294916 

5262  5348  5435 

578i  5868  5954 

63oi  6387  6474 

6821  6908  6995 
587342  7429  7516 

786379508037 

8385  8472  8559 

8908  8995  9082 

g43i  9518I9605 

9955I.  .421. 129 
690479  o566  06 54 

1004*1091  1 179J1266 

1529  1616:1704,1792 

2o55*2l42!223o23l8|24o6  2493120 

,59258i!2669*2757'2845  2932  3020  19 
3io8  3i96!3284J3372|346o3548  18 
37243812  390039884076 
4252I4340  44a8'45i6  46o4 
4781I4869I4957I5045  5i33 
5222  53io  5398  5486  5575  5663 
575i  5840*5928  6017  6io5  6193 
6282  6370  6459  6547  66366724 


2032 
2537 

3o44 
355o 
4o58 
4565 
5073 
5582 
6091 
6601 
7112 
7622 
8i34 
8646 
9i58 
9671 
0184 
0698 

I2l3 

1728 
2243 
2760 
3276 
3793 
43n 
4829 
5348 
5868 
6387 
6908 
7429 

795° 
8472 


7081 
7603 
8124 


.217 
0741 


3636 

4i64 
4692 


3966  4o52  4i 38 
448445704657 
5oo2  5089*5175 
552i  56o8|5694|33 
6o4i  6127  6214  32 
656i  6648!6734  3i 
7i68J7255|3o 
7690  7776  29 
821^829828 
8647J8734|882i  27 
9169J92579344  26 
9693  9780  9867  25 
.3o4  .391  24 
0829  0916  23 
i354  i44i  22 
1879  1967121 


68 1 3  6901  6990  707$ 


716717356  1 1 
7699  77s s  10 

9 

8 


823l  8  32C 

8764  8853 

9298  9387 

9832  9921 


7344  7433  7V22  76IO 

,597876  7965  So548i43 
8409849885878675 
8942  90  i  1  9120  9209 
9476  9565  965419743 

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o545 p635  0724  <)Si  3  0902  0992 
1081I1170  1260  1 349!  x438  1S28 
1617  1706  1 796  t885  1975  2064 
2i54  2243  2333  24222512  2601 
2691 1278 1  287012960  3o5o  3i 39 


I   8  16  2.")  33  41  40  57 


9  ' 
71 


10" 


Co-tangent  of  14  Decrees. 


V  Part 


i  1"    2" 
}   9     17 


:»"    4"    5"    6"    7"    8"    9" 
2fi    35    43    52    61    69   78 


100 


Logarithmic    JSines. 


i 

Sine  of  76  Degrees. 

1 

Sine  of  77  Degrees. 

0" 

10" 

20" 

30" 

40"  1  50" 

0" 

10" 

20"  1  30" 

40" 

50" 

o 

9.986904 

6909 

6915 

6920 

6925I6930  59 

O 

9.988724 

8729 

8734I8739 

8743 

8748 

59 

I 

6g36 

6941 

6946 

6g5i 

6957 

6962 

58 

I 

8753 

8758 

87638768 

8772' 

8777 

58 

2 

6967 

6972 

6978 

6983 

6988 

6993 

57 

2 

8782 

8787 

8792 

8797 

8802 

8806 

57 

3 

6998 

7004 

7009 

7014 

7019 

7025 

56 

3 

8811 

8816 

8821 

8826 

883i 

8835 

56 

4 

7o3o 

7o35 

7040 

7045 

7o5i 

7o56 

55 

4 

884o 

8845 

885o8855 

8860 

8864 

55 

5 

7061 

7066 

7072 

7077 

7082 

7087 

54 

5 

8869 

8874 

88798884 

8889 

8893 

54 

6 

7092 

7098 

7Io3 

7108 

7ii3 

7118 

53 

6 

8898 

8903 

89088913 

8918 

8922 

53 

7 

7124 

7129 

7134 

7i39 

7i44 

7i5o 

52 

7 

8927 

8932 

89378942 

8946 

895i 

5a 

8 

7i55 

7160 

7i65 

7170 

7176 

7181 

5i 

8 

8956 

8961 

8966  8970 

8976 

8980 

5i 

9 

7186 

7191 

7196 

7202 

7207 

7212 

5o 

9 

8985 

8990 

8994 

8999 

9004 

9009 

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IO 

9.987217 

7222 

7228 

7233 

7238 

7243 

49 

IO 

9.989014 

9018 

9023 

9028 

900a 

9o38 

49 

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7248 

7253 

7259 

7264 

7269 

7274 

48 

11 

9042 

9047 

9052 

9o57 

9062 

9066 

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12 

7279 

7284 

7290  7295 

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73o5 

47 

12 

9071 

9076 

9081 

9085 

9090 

9095 

47 

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7310 

73i5 

732117326 

733i 

7336 

46 

i3 

9100 

9105 

9109 

91 14 

9119 

9124 

46 

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734i 

7346 

7352  7357 

7362 

7367 

45 

i4 

9128 

9i33 

9i38 

9i43 

9i48 

9152 

45 

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7372 

7377 

73837388 

7393 

7398 

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9l57 

9162 

9167 9171 

9176 

9181 

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16 

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9190 

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9205 

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7454 

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17 

9214 

9219 

9224 

9228 

9233 

9238 

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18 

7465 

7470 

7475  7480 

7485 

7490 

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18 

9243 

9247 

9252 

9257 

9262 

9266 

4i 

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7496 

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75o6  7511 

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9281 

9285 

9290 

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20 

9.987526 

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7537J7542 

7547 

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39 

20 

9.989300 

93o4 

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93i4 

9318 

9323 

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21 

7557 

7562 

75677572 

7577 

7583 

38 

21 

9328 

9333 

9337 

9342 

9347 

9352 

38 

22 

7588 

7593 

7598  7603 

7608 

76i3 

37 

22 

9356 

9361 

9366 

937o 

9375 

9380 

37 

23 

7618 

7623 

7628  7634 

7639  7644 

36 

23 

9385 

9389 

9394 

9399 

94o3 

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36 

24 

7649 

7654 

7659  7664 

7669  7674 

35 

24 

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9417 

9422 

9427 

9432 

9436 

35 

25 

7679 

7684 

7690  7695 

7700 

77o5 

34 

25 

944i 

9446 

945o 

9455 

9460 

9464 

34 

26 

7710 

77i5 

7720,7725 

773o 

7735 

33 

26 

9469 

9474 

9479 

9483 

9488 

9493 

33 

27 

7740 

7745 

77507756 

7761 

7766 

32 

27 

9497 

9502 

95o7 

95n 

95i6 

9521 

3a 

28 

7771 

7776 

77817786 

7791 

7796 

3i 

28 

9525 

953o 

9535 

9539 

9544 

9549 

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29 

7801 

7806 

7811  7816 

7821 

7826 

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29 

9553 

9558 

9563 

9568 

9572 

9577  3o 

3o 

9.987832 

7837 

7842  7847 

7852  7857 

29 

3o 

9.989582 

9586 

959i 

9596  9600 

9605  29 

3i 

7862 

7867 

7872.7877 

7882  7887 

28 

3i 

9610 

9614 

9619 

9623I9628 

9633 

28 

32 

7892 

7897 

7902  7907 

7912 

7917 

27 

32 

9637 

9642 

9647 

965i 

9656 

9661 

27 

33 

7922 

7927 

79327937 

7942 

7947 

26 

33 

9665 

9670 

9675 

9679 

9684 

9689 

26 

34 

7953 

7958 

7963  7968 

7973 

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25 

34 

9693 

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9740J9744 

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23 

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98189823 

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39 

8io3 

8108 

8ii38n88i23 

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20 

39 

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9846 

985o 

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4o 

9.988133 

8i38 

8i438i488i53 

8i58 

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9.989860  9864I9869 

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8i63 

8168 

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18 

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9887 

9892  9896 

9901 

9906 

9910  18 

42 

8193 

8198  8203  8208  8213I8218 

17 

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9929 

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8223 

822782328237I8242I8247 

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43 

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9947  9952 

9956  9961 

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44 

8252 

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82628267182728277 

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997°9974|9979 

99849988 

9993  i5 

45 

8282 

8287 

8292  8297  83o2  8307 

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. . 1 1  .  .16 

.  .20  14 

46 

83i2 

83i7 

8322l83278332  8337 

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9.990025 

0029  oo34 

oo38  oo43 

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47 

8342 

8346 

835i  8356!836i 

8366 

12 

47 

0052 

0057  0061 

0066  0070 

0075:12 

48 

837i 

8376 

838i  8386!839i 

8396 

1 1 

48 

0079 

00840088 

0093  0098 

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49 

84oi 

84o6 

84ii'84i6  842o 

8425 

IO 

49 

0107 

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0116 

0120 

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9.988430 

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9.990134 

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8484 

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8 

52 

8489 

8494 

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85i4 

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0188 

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0197 

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53 

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8529!8534!8538 

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53 

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0220 

0225 

0229 

0234 

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0243 

0247 

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0261 

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60"    |  50" 

40" 

30"  |  20" 

10" 

a 

60"    j  50"  |  40" 

30"  |  20"  |  10" 

j 

Co-sine  of  13  Degrees. 

Co-sine  of  12  Degrees. 

s 

P. 

v     ,51"  2"  3"  4"  5"  6"  7"  8"  9" 
lalt\    1   1   2   2   3   3   4  4      0 

P. 

(1"  0"  3"  4"  5"  G"  7"    8"  9" 
a>01122   33   4   4 

LOQAEITHMIC     T  A  N  0  E  N  T  3. 


101 


Tangent  of  76  Degrees. 


20"   30"   40"   50" 


Tangent  of  77  Degrees. 


10"  |  20"  I  30"   40"   50" 


10 


10 


o 
I 

2 

3 

4 
5 
6 

7 

8 

9 

10 

ii 

19 

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22 
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29 
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2008 

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P.  1'art 


<  1"    2"    3" 
^9     19    2S 


4" 
37 


5"    6"    7"    *      U 
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4"    5"    fi"    7"    8"    9" 
30    40    50    GO    70    80    90 


102 

L 

OGARITHMIC  ISlNES. 

s 

Sine  of  78  Degrees. 

a 

2 

Sine  of  79  Degrees. 

0"    j  10"  |  20"  1  30"  |  40"  |  50" 

O'' 

10" 

20" 

30" 

40'' 

50" 

1  . 

o 

9.990404I04090413  o4i8  0422 

0427 

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0 

9.991947 

1 95 1 

1955 

i959 

1963 

1967 

59  ' 

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o43 1  p436|o44o  o445 

o449 

o454 

58 

I 

1971 

1975 

1979 

1983 

1987 

I992 

58 

a 

o458|o462;'o467  0471 

0476 

o48o 

57 

2 

1996 

2000 

2004 

2008 

2012 

2016 

57 

3 

o485 

0489:0494:0498 

o5o3 

0507 

56 

3 

2020 

2024 

2028 

2032 

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2040 

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2073 

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5i 

9 

o645 

o649o653Jo658 

0662 

0667 

5o 

9 

2166 

2I7O 

2174 

2178 

2182 

2186 

5o 

IO 

9.990671 

0675  0680  0684 

0689 

0693 

49 

10 

9.992190 

2194 

2198 

2202 

2206 

2210 

49 

:i 

0697 

0702  0706  071 1 

0715 

0719 

48 

11 

22l4 

22l8 

2222 

2226 

223o 

2234 

48 

12 

0724 

0728  0733,0737 

0741 

0746 

47 

12 

2239  2243 

2247 

225l 

2255 

2259 

47 

i3 

0750 

0755  0759  0763 

0768 

0772 

46 

i3 

2263 

2267 

227I 

2275 

2279 

2283 

46 

i4 

0777 

0781  0785  0790 

0794  0798 

45 

i4 

2287 

229I 

2295 

2299 

23o3 

2307 

45 

i5 

o8o3 

0807  081210816 

0820 

0825 

44 

i5 

23ll 

23i5 

2319 

2323 

2327 

233i 

44 

16 

0829 

o833'o838o842 

0847 

o85i 

43 

16 

2335 

2339 

2343 

2347 

235i 

2355 

43 

17 

o855 

086008640868 

o873 

0877 

42 

17 

2359 

2363 

2366 

2370 

2374 

2378 

42 

18 

0882 

08860890  0895 

0899 

0903 

4i 

18 

2382 

2386 

2390 

2394 

2398 

2402 

4i 

J9 

0908 

0912  0916 

0921 

0925 

0929 

4o 

*9 

2406 

2410 

2414 

24l8 

2422 

2426 

4o 

20 

9.990934 

09380942 

0947 

0951 

0955 

39 

20 

9.992430 

■2434 

2438 

2442 

2446 

245o 

39 

21 

0960 

0964  0969 

o973 

0977 

0982 

38 

21 

2454 

2458 

2462 

2466 

2470 

2474 

38 

22 

0986 

0990  0995 

0999 

ioo3 

1008 

37 

22 

2478 

2482 

2485 

2489 

2493 

2497 

37 

23 

1012 

1016  1021 

I025 

1029 

io33 

36 

23 

25oi 

25o5 

2509 

25i3 

2517 

2521 

36 

24 

io38 

1042  1046 

io5i 

io55 

1059 

35 

24 

2525 

2529 

2533 

2537 

254i 

2545 

35 

25 

1064 

1068:1072 

1077 

1081 

io85 

34 

25 

2549 

2553 

2556 

256o 

2564 

2568 

34 

26 

1090 

1094  1098 

no3 

1107 

IIII 

33 

26 

2572 

2576 

258o 

2584 

2588 

2592 

33 

27 

iii5 

1120,1124 

1128 

n33 

n37 

32 

27 

2596 

2600 

2604 

2607 

2611 

26i5 

32 

28 

n4i 

1146^150 

u54 

n58 

n63 

3i 

28 

2619 

2623 

2627 

263i 

2635 

2639 

3i 

29 

1167 

1171  1176 

1 1 80 

1 184 

1188 

3o 

29 

2643 

2647 

265i 

2654 

2658 

2662 

3o 

3o 

9.991193 

1197  1201 

1206 

1210 

1214 

29 

3o 

9.992666 

2670 

2674 

2678 

2682 

2686 

29 

3i 

1218 

1223  1227 

I23l 

1235 

1240 

28 

3i 

2690 

2693 

2697 

2701 

2705 

2709 

23 

32 

1244 

1248  1253 

1257 

1261 

1265 

27 

32 

2713 

2717 

2721 

2725 

2728 

2732 

27 

33 

1270 

1274  1278 

1282 

1287 

1291 

26 

33 

2736 

2740 

2744 

2748 

2752 

2756 

26 

34 

1295 

12991304 

i3o8 

l3l2 

i3i6 

25 

34 

2759 

2763 

2767 

2771 

2775 

2779 

25 

35 

l32I 

i325  1329 

i333 

i338 

1 342 

24 

35 

2783 

2787 

2790 

2794 

2798 

2802 

24 

36 

1 346 

i35o  1 355 

i359 

i363 

1367 

23 

36 

2806 

2810 

2814 

2818 

2821 

2825 

23 

37 

1372 

1376  i38o 

1 384 

i389 

i393 

22 

37 

2829 

2833 

2837 

2841 

2845 

2848 

22 

38 

i397 

i4oi 

i4o6 

i4io 

i4i4 

i4i8 

21 

38 

2852 

2856 

2860 

2864 

2868 

2871 

21 

39 

1422 

1427 

i43i 

i435 

i439 

i444 

20 

39 

2875 

2879 

2883 

2887 

2891 

2895 

20 

4o 

9.991448 

1452 

i456 

i46o 

i465 

1469 

19 

4o 

9.992898 

2902 

2906 

2910 

2914 

2918 

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4i 

1473 

1477 

1482 

i486 

i49o 

i494 

l8 

4i 

2921 

2925 

2929 

2933 

2937 

2941 

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42 

1498 

i5o3 

1 507 

1 5  i'i 

i5i5 

1519 

17 

42 

2944 

2948 

2952 

2956 

2960 

2963 

17 

43 

i524 

i528 

1 532 

i536 

1 54o 

1 545 

l6 

43 

2967 

2971 

2975 

2979 

2983 

2986 

l6 

44 

1 549 

i553 

i557 

i56i 

i566 

1570 

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44 

2990 

2994 

2998 

3002 

3oo5 

3009 

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45 

i574 

i578 

i582 

i586 

i59i| 

i595 

14 

45 

3oi3 

3017 

3021 

3024 

3028 

3o32 

U 

46 

1 599 

i6o3 

1607 

1612 

1616 

1620 

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46 

3o36 

3o4o 

3o43 

3o47 

3o5i 

3o55 

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47 

1624 

1628 

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i637 

i64i! 

i645 

12 

47 

3o59 

3o6a 

3o66 

3070 

3074 

3078 

12 

48 

1649 

i653 

1657 

1662 

1666 

1670 

1 1 

48 

3o8i 

3o85 

3089 

3093 

3o97 

3 1 00 

11 

49 

1674 

16781682 

1687 

1 69 1 

i695 

10 

49 

3io4 

3io8 

3na 

3n5 

3119 

3i23 

IO 

5o 

9.991699 

17031707 

1712 

1716 

1720 

9 

5o 

9.993127 

3i3i 

3i34 

3i38 

3i42 

3i46 

9 

5i 

1724 

1728  1732 

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i74i' 

1745 

8 

5i 

3 1 49 

3i53 

3i57 

3i6i 

3i65 

3i68 

8 

52 

1749 

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i757 

1761 

1765; 

[770 

7 

52 

3172 

3i76 

3i8o 

3i83 

3i87 

3191 

7 

53 

1774 

1778 

1782 

1786 

1790 

1794 

6 

53 

3195 

3198 

3202 

3206 

32IO 

32i3 

6 

54 

1799 

i8o3 

1807 

1811 

i8i5 

1819 

5 

54 

3217 

3221 

3235 

3228 

3232 

3236 

5 

55 

1823 

1827 

1 832 

i836 

i84o! 

1 844 

4 

55 

324o 

3243 

3247 

325i 

3255 

3258 

4 

56 

1 848 

i852 

i856 

i860 

i865 

[869 

3 

56 

3262 

3266 

3270 

3273 

3277 

3281 

3 

57 

i873 

1877 

1881 

i885 

1889 

i893 

2 

5? 

3284  3288 

329213296 

3299 

33o3 

2 

58 

1897 

1901 

1906 

1910 

1914 

1918 

1 

58 

3307  33n 

33i4'33i8 

3322,3325 

I 

59 

1922 

1926 

1930 

1934 

i938 

1942 

0 

59 

3329  3333 

3337!334o| 

33443348  0 

60" 

50"  1  40" 

30"  |  20"   10" 

60"    |  50"  j  40"  1  30"  |  5J0"  |  10" 

• 

Co-s 

jne  of  11  Degrees. 

Co-sine  of  10  Degrees. 

S 

P. 

Ho ' 

1"    3"  4"  5"  6"  7"    8"  9" 
1   12   2   3   3   3   4 

P. 

p  .(1"  2".  3"  4"  5"  G"  7"  8"  9" 
{   0      1   12   22   334 

MM 

Logarithmic    Tangents. 


103 


Tangent  of  78  Degrees. 


10"       20"       30"       40"   |  '50" 


Tangent  of  79  Degrees. 


10"  j  20"   30"   40"   SO" 


o  io.(J72525J262QJ2733'2836 


9 
to 

1 1 

t  a 

i3 

i4 
i5 

iG 

17 

is 

*9 

2n 
2  1 
22 

-■; 

24 

2  5 
2f 

27 
28 

»9 

3d 

3 1 

:i 
33 
34 
35 
36 

37 

38 

39 

4o 
4i 
42 
43 
44 
45 
46 
4? 
4- 

49 

5o 

5i 
5a 

53 
54 
55 
56 

57 

58 

59 


773i 
8359 


9618 
0249 
0881 
i5i4 
2147 


3458 
4o8i 
47o5 
5329 
5954 
658o 
7207 
7835 
8464 
9093 
9723 
o355 
0987 
1619 

2253 

2887 

3523 
4159 
4796 


2940  3o43 
3562J3666 
41854289 
480949:3 
54335537 
60596163 


3i47  325i  3354 

37693873:3977 

439S U497  46oi 

5oi7|5i2i  5225 

564215746  585o 

626716372  6476 

6894J6998  7103 

7521  7626 

81498254 

87788883 

9408  95i3 
10.680039  oi44 

0670  0776 

i3o3  1408, 

1936  2042 

257o'2676'2782 

32o5  3311I3417 

384i  3947J4053 

4477  4584T469o 

5u5  5221  532815434 

5753[586o|5966  6073 

6392 J6499J6606  6712 

7032I7139  7246  7353 

7673 1 7780! 7887  7994 

83i5J8422'8529!8636 

8958  9065,9172  9280I9387J9494 

96oiJ9709!98i6  9924I. . 3i 1 . 1 38 
10  690246J0353I0461. 

089 1 10999  1  io7 

i537  i645  1753 

2184,2292.2400 

283212941  3o49 

3481I35903698 

4i3i  42394348 

4782  48904999 

54335542565i 

608J6  6195  63o3 

673968486957 


66856789 
7312  7417 
7940  8o45 
85698674 
9198  93o3 
98299934 
0460  o565 
1092I1197 
1725  i83o 
23592464 
2993^099 
36293735 
42654371 
4902  5009 
554o  5647 
6179  6286 
6819  6926 
7460  7567 
8101  8208 
87448851 


o568  0676  0784 
1214  i322  i43o 
:86i  1969  2077 
25o8  261612724 
3i5732653373 
38o6  3914  4o23 
445645654673 
510715216  5325 
575958685977 
64:26521  663o 
706617175  7284 
7393!  75o3J  76 12!  7721  78307939 
8049,8158  8267J8376  8486'8595 
8705188148924903391439252 
9362  9471  9581  9691  9800, 99 10 
,700020,0129:0239  o349  0459,0369 
06780788:0898  1008  11 18J 1 228 
i338i448|i558  1668  1779  1889 
1999,2109  2219  233o  244o;255o 
2O61  2771  2881  2992  3io2J32i3 
3323,3434  354413655 
398714097142084319 
465i  4762I4873J4984 
53i6!5427|5538|5649 
5983,6o94|62o5 ,63 1 6 
6G5.V0761I6S736984 


73i8,743o|754i  7653 

7987  8099  8211  8322 

8658J87698881  8993 

*9329  94419553  9665 

IO.  7  I  OOO I  [oi  I  3!  0225 io337 
0674I0786J08981IOI  I 


vy 


3765  3876 
44^9,454o 
5o95j52o5 
5761  5872 
64286539 
7095  7207 
7764I7876 
84348546 
9105I9217 

9777  9889 
i)44y  o562 
1 12'i  1235 


Co-tanpent  of  1 1  Degrees. 


P.  Pa 


rtJ  '"  ~" 
I   11  22 


5  I 


6" 

65 


8" 
86 


10.711348 

2023 
2699 
3376 

4o53 
4732 
54i2 
6093 
6775 
7458 
8142 
8826 
9512 

10.720199 
0887 
1576 
2260 
2957 
3649 
4342 
5o36 
573i 
6427 
7124 
7822 
852i 
9221 
9923 

10.730625 
1 329 
2o33 
2739 
3445 
4i53 
4862 
5572 


1460  1573 
2i35  22 
281 1  2924 
3488  36oi 
4167  4280 
4846  4959 


5526 
6207 


5639 
632o 


3072 
3764 
4457 
5i5i 
5847 


6889  7002 
7572  7686 
82568370 
8941  9055 
96279741 
o3i4  0428 
1002  1 1 16 
1 69 1 
238i 


1806 
2496 
3187 
3879 
4573 
5267 
5963 


6543  6659 

7240  7356 
7g388o55 
8638  8754 
9455 
i57 


9338 

.4o 

0742 

1 446 

2l5l 

2856 

563 

4271 

4980 


0860 
i563 
2268 
2974 
368i 
4389 
5oo8 


5690  5809 


652o 
7232 


6283:64oi 
6995 71 13 

7708  7827 
8422  854i 
9l37  9=57'9376 


1 685 
236i 
3o37 
37i4 
4393 
5072 
5752 
6434 
7116 

7799 

8484 

9169 

9856 
o543 

I23l 

1921 
2611 
33o2 
3995 
4688 
5383 
6079 
6775 
7473 
8171 
8871 
9572 
.274 
0977 
1681 
2386 
3092 
3799 
45o7 
5217 
5927 
6639 
735i 


1798 
2473 
3i5o 
3827 
45o6 
5i85 
5866 
6547 
723o 
79i3 
8598 
9283 
9970 
o658 
1 346 


1910P9 
2586J58 
3a63p7 
3940  56 
46i955 
529954 
5979P3 
666i!52 
73445i 
027:5o 
8712U9 
9398  48 


.85 
0772 
i46i 


2o36,2i5i 
2726:2841 
34I8J3533 
4no 

4804 
5499 
6195 
1 

7589 

8288 


4226 
4920 
56i5]39 
63u  38 
7008  37 
7706  36 
84o535 
9io5i34 
9689!98o633 


391 
1094 
1798 
25o3 


7946  8o65 

866018780 

9496 


2l3 

0931 


i65o 


9854:99731 .  .93 
10.740571  0691  081 1 
1290  i4io  i53o 
2010  2i3o  225o 
2731I2851  2971 
3453|3573|3694| 
4i76J4297j44i7|4538 
49oo5o2i|5i42:5263 
5626|5747j5S68J5989 


5o8  3a 
121 1  3i 
igie^o 
2621  29 
3210I332728 
3917  U035J27 
46a5  4744)26 
5335545325 
6046616424 
67576876133 
7470J7589  22 
8i84'83o3  2i 
8899  9018:20 
960  9734  19 
3321.452  18 
io5o  1170 
1770 1890 


370  2490  261 1 


3092 
38i4 


6352|G473f6595 
70807201  7323 
7809  793oi8o52 
853y866i  8782 
927019392  9514 


6716 

7444 
8174 


55 1 1 0.750002  0124I0247  0369 


3212  333 
3935  4o55i3 

4659!477V  Ia 
5384  55o5  11 
6110  623i  10 
6837  6959]  9 
756676S7 
82958417 
89o4'9026  9148 
9636'9758.988o 


0736  o858  0980  1  io3 
1470  1 5931 1715  i838 
2206  2329  2452  2^74 
2943;3o66;3i89!33i2 


0491  061 3 
i225'i348 
1961J2083 
2697  2820 
3435  3558 


.V)""!  40"  I  30" 


10* 


Co-tangent  of,  10  Degrees. 

7" 


,  p    ,  <  1"   2"    3"    1"    5"    6"    7"    8" 
•lurt$  12  23    35    47    59    70    82    91 


9" 

106 


104 


Logarithmic    Sine  a. 


o 

i 

3 
4 
5 
6 

7 
8 

9 

10 

1 1 

12 

i3 

i4 
i5 

iG 

17 
1 8 

*  9 

20 

21 
22 

2  3 
24 
25 
26 

27 

28 
29 

3o 
3i 

3  a 

33 
34 
35 
36 

3? 
38 
39 
4o 
4i 
42 
43 
44 
45 
46 

47 

48 

49 
5o 

5i 

52 

53 
54 
55 
56 

5? 
58 
59 


Sine  of  80  Degrees. 


9.993351 
3374 
3396 
34i8 
344o 
3462 
3484 
35o6 
3528 
355o 

9.993572 
3594 
36i6 
3638 
366o 
368i 
37o3 
3725 
3746 
3768 

9.993789 
38n 
3832 
3854 
3875 
3897 
3918 
3939 
3960 
3982 

9.994003 
4024 
4o45 
4066 
4o87 
4108 
4129 
4i5o 
4i7i 
4191 

9.994212 
4233 
4254 
4274 
4295 
43i6 
4336 
4357 
4377 
4398 

9.994418 
4438 
4459 
4479 
4499 
4519 
454o 
456o 
458o 
46oo 


60" 


3355 
3377 
34oo 
3422 
3444 
3466 
3488 
35io 
3532 
3554 
3576 
3598 
3620 
364i 
3663 
3685 
37o7 
3728 
375o 
377i 
3793 
38i4 
3836 
3857 
3879 
3900 
392i 
3943 
3964 
3985 
4oo6 

4027 

4o48 
4069 
4090 
4i  1 1 

4l32 

4i53 
4i74 
4195 
4216 
4236 
4257 

4278 

4298 
4319 
434o 
436o 
438i 
44oi 
4421 
4442 
4462 
4482 
45o3 
4523 
4543 
4563 
4583 
46o3 


20"   30'   40"   50" 


3359 

338i 
34o3 
3426 
3448 
347o 
3492 
35i4 
3536 
3558 
358o 
36oi 
3623 
3645 
3667 
3689 
37io 
373 


3363 
3385 
34o  7 
3429 
345 1 
3473 
3495 
35i7 
3539 
356i 
3583 
36o5 
3627 
3649 
367o 
3692 
37i4 
3735 


3753j3757 
3775,3779 
3797|38oo 
38i8|3822 
384o3843 
386i!3864 
3882^3886 
3904J3907 
392513928 
3946j395o 
3967I3971 
398913992 
4oio'4oi3 
4o3ij4o34 
4o52  4o55 
4o73  4o76 
4094  4o97 
4ii5'4n8 
4i36!4i39 
4i57  4i6o 
4i784i8i 
41984202 
4219  4223 
4240  4243 

426IJ4264 
4281  4285 

43o2  43o5 

4322^326 

4343  4346 


4363 

4384 
4464 
4425 


4367 
4387 
44o8 
4428 


4445|4448 
4465 14469 
4486J4489 
45o6  4509 


4526 
4546 
4566 
4587 
46o7 


453o 
455o 
457o 
4590 
4610 


3366 
3389 
34n 
3433 
3455 
3477 
3499 
352i 
3543 
3565 
3587 
3609 
363i 
3652 
3674 
3696 
37i7 
3739 
376i 
3782 
38o4 
3825 

3847 
3868 


3911 
3932 
3g53 

3974 
3996 

4017 

4o38 
4059 
4o8o 
4ioi 

4l22 

4i43 
4i64 
4i84 
42o5 
4226 
4247 
4267 
4288 
4309 
4329 
435o 
4370 
4391 
44n 
4432 
4452 
4472 
4492 
45i3 
4533 
4553 
4573 
4593 
!46i3 


3370 
3392 
34i4 
3437 
3459 
3481 
35o3 
3525 
3547 
3569 
3591 
36i2 
3634 
3656 
3678 
3699 
3721 
3743 
3764 
3786 
3807 
3829 
385o 
3872 
3893 
3914 
3936 
3957 
3978 
3999 

4020 

4041 
4062 
4o83 
4io4 
4i25 
4i46 
4167 
4i88 
4209 
423o 
425o 
4271 
4292 
43i2 
4333 
4353 
4374 
4394 
44i5 
4435 
4455 
4476 
4496 
45i6 
4536 
4556 
4576 

4597 
4617 


Co-sine  of  9  Degrees. 


Sine  of  81  Degrees. 


9.994620 
464o 
466o 
468o 
4700 
4720 
4739 
4759 
4779 
4798 

9.994818 
4838 
4857 
4877 
4896 
49-6 
4935 
4955 
4974 
4993 
99501 3 
5o32 
5o5i 
5070 
5089 
5io8 
5127 
5i46 
5i65 
5i84 
995203 

5222 
524l 
526o 

5278 
5297 

53i6 
5334 
5353 
5372 

995390 
5409 
5427 
5446 
5464 
5482 
55oi 
5519 
5537 
5555 

995573 
5591 
56io 
5628 
5646 
5664 
568 
5699 
57i7 
5735 


4623 
4643 
4663 
4683 
47o3 

4723 

4743 

4762 

4782 

4802 
4821 
484i 
4861 
4880 
4900 

49T9 
4938 
4g58 
4977 
4997 
5oi6 
5o35 
5o54 
5o73 
5092 

5lI2 

5i3i 

5i5o 
5169 
5i88 
5206 

5225 

5244 
5263 
5282 
53oo 
53ig 
5338 
5356 
5375 
53g3 
54i2 
543o 
5449 
5467 
5485 
55o4 

5522 

5540 

5558 
5576 
5594 
56i3 
563i 
5649 
5667 
5684 
5702 
5720 
5738 


4627 
4647 

4667 

4686 
4706 
4726 
4746 

47& 
48o5 
4825 
4844 
4864 
4883 
4903 
4922 
4942 
4961 
4980 
5ooo 
5019 
5o38 
5o57 
5o77 
5096 
5n5 
5i34 
5i53 

5l72 

5191 

52IO 

5228 

5247 

5266 
5285 
53o3 

5322 

534i 
5359 
5378 
5396 
54i5 
5433 
5452 
547o 
5488 
55o7 
5525 
5543 
556i 
5579 
5597 
56i6 
5634 
5652 
567o 
5687 
57o5 

572^ 

574i 


463o 
465o 
467o 
4690 
47io 
4729 
4749 
4769 
4789 
48o8 
4828 
4848 
4867 
4887 
4906 
4926 
4945 
4964 
4984 
5oo3 

5022 

5o4i 
5o6i 
5o8o 
5099 
5n8 
5i37 
5i56 
5i75 
5i94 
52i3 

5232 

525o 
5269 
5288 
53o7 
5325 
5344 
5362 
538i 
5399 
54i8 
5436 
5455 
5473 
549i 
55io 
5528 
5546 
5564 
5582 
56oi 
5619 
5637 
5655 
5672 
5690 
57o8 
5726 
5  744 


4633 
4653 
4673 
4693 
47i3 
4733 
4752 
4772 
4792 
48i2 
483i 
485i 
4870 
4890 
4909 
4929 
4948 
4968 

4987 
5oo6 
5o25 
5o45 
5o64 
5o83 
5 1 02 

5l2I 

5i4o 
5i  59 
5i78 
5i97 
5216 
5235 
5253 
5272 
5291 
53io 
5328 
5347 
5365 
5384 
54o3 
5421 
5439 
5458 
5476 
5494 
55i3 
553i 
5549 
5567 
5585 
56o4 
5622 
564o 
5658 
5675 
56g3 
57n 
5729 
5747 

30" 


4637  59 

465758 

4676  57 

4696 

4716 

4736 

4756 

4776 

4795 

48i5 

4834 

4854 

4874 

4893 

49i3 

4932 

495i 

4971 

4990 

5009 

5029 

5o48 

5067 

5o86 

5io5 

5 1 24 

5i43 

5 1 62 

5i8i 

5200 

5219 
5238 
5257 
5275 
5294 
53i3 
533i 
535o 
5369 
5387 
54o6 
5424 
5442 
546i 

5479 
5497 
55i6 
5534 
5552 
5570 
5588 
5607 
5625 
5643 
566i 
5678 
5696 
57i4 
5732 
5750 


56 
55 
54 
53 

52 

5i 

5o 

49 

48 

47 
46 
45 
44 
43 
42 
4i 
4o 
3o 
38 
37 
36 
35 
34 
33 

32 

1 
3o 
39 

28 
27 
26 

25 

■M 

2  3 
2  2 
23 
20 

*9 

18 

17 
16 
i5 
14 
1 3 
12 
11 
10 


Co-sine  of  8  Degrees. 


p  p    .«1"   2"    3"    4"    5"    6"    7" 
1.1  artj   0111222 


8"    9" 
3      3 


P  P    A  I"   2"    3"    4"    5"    6"    7"    8"    D" 
i.rart^   0      1      1      1      2      2      2      3      3 


Logarithmic    Tangents. 


105 


Tangent  of  80  Degrees. 


10"   20"   30"   40"   50" 


0" 


Tangent  of  81  Degrees. 

1  40"  j~50"" 


10" 


9 

10 

ii 
ia 

i3 

i4 
i5 
16 
17 

IS 

19 

20 
21 
22 

23 
24 

a  6 

27 
28 
a9 
3o 
Si 
3  a 
33 
34 
35 
36 

37 
38 
39 
4o 

4i 

42 

43 

44 
45 
46 

47 
4* 

49 

5,. 

5i 
5  a 

53 
54 
55 
56 

57 
58 
59 


10.753681 
44si 
5i6i 
5903 
6646 
739o 
8i35 
8882 
9629 

10.760378 
1128 
1880 

2632 

3386 

4i4i 

4897 
5655 
64i4 
7174 
7935 


38o4 
4544 
5285 
6026 


3928 
4667 
54o8 
6i5o 


946i 
10.770227 
0993 
1761 
2529 


6770  6894 
75i47638 
82598384 
9006  9131 


9754 
o5o3 
1253 
2oo5 
2758 
35i2 
4267 
5o24 
578i 
654o 
7301 
8062 
8825 
9589 
o354 
1121 
1889 


9879 
0628 
i379 
2i3o 
2883 
3638 
4393 
5i5o 
5908 
6667 


4o5i  4174U297 
4791 U914  5o38 
553256555779 
6274  639816522 
7018  7142(7266 
7762  7886|8on 
85o8j8633  8757 
9255  9380  95o5 
.4  .128  .«53 
07530878  ioo3 


i5o4 

2256 

3009 
3763 
4519 
5276 
6o34 
6794 


7427  h554 
81898316 
8952  9079 
9716  9844 


0482 
1249 
2017 


33oo3428 
4071  4200 

4844J4973 
56i8j5747 
6393  6523 


7170 
7948 
8728 
95o8 
.780290 
1074 
i858 
2644 
3432 
4220 
5on 
58o2 
65g5 


73oo 


0610 
1377 
2i45 
2914 
3685 
.  4457 
5io2J523i 
5876  6006 
6652  6782 


658  2786 
3557 
4329 


7429 


80788208 
88588988 


9639 
0421 

I204 
I989 
2775 

3563 
4352 
5i42 


9769 
o55i 
i335 
2120 


7559 
8338 
9118 
9899 
0682 
i486 

225l 

3o38 
3826 
46i5 


1629  1754 
238i  2507J48 
3i35326o47 
3889!4oi5  46 
4645|477i  45 
54025529144 
'43 
42 
4i 
4o 

39 

38 

37 

3(3 


2907 

3695 

4484( 

5274|54o6 

5934I6066.6198 

.    6727:6859^992 

7389,7522|7654  7787 

8i85|83i7'845o'8583 


6i6i'6287 
692017047 
7681J7808 
8443  8570 
9207:9334 
9971  ..99 
0737:0865 
i5o4ii632 
2273|24oi|35 
3o43!3i7i  34 
38i4l394233 
4586J47i5|32 
3i 
3o 
29 
28 

43 
26 
15 

24 

23 

22 

21 


536o!5489 
6i35|6264 
691 1  7041 
76897818 
8468J8598 
9248  9378 
9  .160 
0812^0943 
1 5971727 


2382  25i3 
3169  33oo 
3957|4o89|2o 
47474879  19 
5538  567o|i8 


2:9115^2 
97809913.  .46 
10. 790580^713  0847 


9381 
180 


1 648 
245i 
3256 


1 38 1 1 1 5 1 5 

2i83  a3i7 

2987.3133 

3793:39274063 

46oo!4734l4869 

54o8|5543,5678 

6318  6353,6488 


633o,6463 

7124  7257 


7919  8o52 
87168849 
95i4  9647!  1 3 
.3i3|.446  12 
0980J11141247  11 
1783  1916  3o5o  10 
2585  3719  2853  9 
339o35a43658 
4i96  433i;4465 
5oo45i38  5273 
58i3j5947'6o82 
66s3  6758  6893 


7029  7164  72991743517570  7706 
7841  797781138248  8384  85i9 
8655,8791892790639199  9335 
9471  9607  9743  98791 . .  i5  . 1 5 1 


10.800287 
1106 
1926 
2747 
3570 
4394 

5220 
6o47 
6876 
7706 

8538 
937i 

10.810206 
1042 
1880 
2720 
356i 
44o3 
5248 
6093 
6941 
7789 
864o 
9492 

io.82o345 
1201 
2o58 
2916 
3776 
4638 
55oi 
6366 
7233 
8101 
8971 
9843 

10.830716 
1591 
2468 
3346 
4226 
5i68 
5992 


0424 
1242 
2062 


o56o 
i379 
2199 


2884 
3707 
4532 
5358 
6i85 
7014 
7845 
8677 
95io 
o345 
1182 
2020 
2860 
3701 
4544 
5388 
6234 
7082 
793i 
8782 
9634 

o488Jo63o 
i343  i486 
2200  2344 
3o59  32o3 
3920  4o63 
4782  U925 
56455789 
65n  6655 
7377  7522 
824618391 
9116J9261 
9988.134 
0862  1008 
1737  i883 
2614  2760 
3493j  3639 
4373  452o 
5255j54o2 
613916287 
6877I702517172 
7764  791218060 


302I 

3844 
4669 
5495 
6323 
7152 
7983 
8816 
9649 
o485 

1322 

2160 
3ooo 
3842 
4685 
5529 
6375 
7223 
8073 
8924 
9776 


0696J0833  0969 
i5i6  i652  1789 
233624732610 
3i58  3295(3433 
3982  41194257 
4807  4944j5o82 
5633  577115909 
6599:6738 
7429  7568 


59 
58 

5? 

•36 
55 
r4 
53 
5a 
5i 
826i!8399!5o 


646 1 
7291 
8122 
8954  909319232 


9788 
0624 
i46i 
23oo 
3i4o 
3982 
4825 


5670 

65i7 

7365 

8214 

9066 

9918 

o773 

1629 

2487 

3346J3489 

4207J4350 


9928  ..67 
0764:0903 
1601  1741 
244o  258o 
328oj34ai 
4122  4263 
4966J5107 


58n  5952 
66586799 
7506J7648 
83568498 
9208  93S0 

..6l  .203 

0915  io58 

1772 

263o 


5069 
5933 
6799 
7667 
8536 
9407 
279 
n53 
2029 
2907 


52 1 3 
6078 
6944 
7812 
8681 
9552 


49 
48 

47 
46 
45 
44 
43 
42 
4i 
4o 

39 

38 

37 
36 
35 

34 
33 

32 

3  1 

3o 

29 


1915 
2773 
3633 
4494 
5357 
6222 
7088J28 
7956I27 
8826,26 
969725 
425  . 570^4 
i299|i445|23 

2175  2322  22 

3o53  3200 
3786139334080 

4667!48i4'496i 
555o!5697'5844 
643465826729 
7320I746S  7616 
8208  8356!85o4 


8653  8801 18949-9098 

9543  9692 ^840, 9989 

io.84o435|o584|o733:o882 

1329;  i479j 1 028j  1 777 


j5  2375i2524 
3i23|3272:3422 

4022  4l72  4322 
4923'5074  5224 


2674 
3572 
4472 


Co-tangent  of  9  Degrees. 


p„rtJ  1"    2-'    3"   4"   5"  6"   7"    8" 
1HriJ  13    26    39  52   65  78  91    103 


9" 
llfi 


P.  Part 


9246,9395 
,x38  .287 
io3ijii8o 
1926  3076 
2833'2973 
3723  387a 
4623  4773 
5374!5525  5675 
6826,5977  6127  627^  6429  658o 
673i|6882|7o33  7184  7335  7486 
7637,7789  7940  8091  8243  8394 
8546:8697  8849  90011915a  9304 
9456  9608  9760  991 2|.  .64  .216 
,85o368o52o  0672  08260977  11 29 
'1434  1 587I 1 739  .'892  2045 

30"  \UV'"      !U" 

Co-tangent  of  8  Degrees. 

11    .til     q// 

1  29 


{! 


4"    5" 
43    58   72 


6"    7"     8"     9" 
8fi    101  115  130 


106 


Logarithmic    Sines. 


Sine  of  82  Degrees. 


Sine  of  83  Degrees. 


20"   30" 


50" 


9.995753 
5771 
5788 
58o6 
5823 
584i 
5859 
5876 
5894 
5911 

9.995928 
5946 
5963 
598o 


5756 
5773 
579i 
5809 
5826 
5844 
5862 

5879 
5897 
5914 
5931 
5949 
5966 
5983 
599816001 
6oi5i6oi8 


5759 
5776 
5794 
58i2 
5829 
5847 
5864 
5882 
5899 
59i7 
5934 
§952 
5969 
5986 
6oo3 
6021 
6o32|6o35J6o38 
6049  6o52  6o55 
6066,6069  6072 
6o83  6086  6089 
9 .996100J6103 


61 17  6120 
6i34J6i37 
6i5i  6i54 
6168  6171 


6i85 
6202 
6219 
6235 
6252 
9.996269 
6285 
63o2 
63i8 
6335 
635i 
6368 
6384 
64oo 
3gj  6417 
4o  9.996433 


4i 
42 

43 

a 
45 

46 

47 

48 

49 
5o 

5i 

52 

53 

54 
55 
5G 

57 

58 

59 


6188 
62o5 
6221 
6238 
6255 
6271 
6288 
63o5 
632i 
6338 
6354 
6370 
6387 
64o3 
6419 
6436 
6452 
6468 
6484 
65oo 
65i7 
6533 
6546'6549 
65626565 
6578  658o 


6449 
6465 
6482 
6498 
65i4 
653o 


9.996594 
6610 
6625 
664i 
6657 
6673 


6596 
6612 
6628 
6644 
6660 
6675 
6688J669I 

67046707 
6720  6722 

67356738 


6106 
6123 
6i4q 
6157 
6i74 
6191 
6207 
6224 
6241 
6257 
6274 
6291 
6307 
6324 
634o 
6357 
6373 
6390 
64o6 
6422 
6438 
6455 
6471 
6487 
65o3 
6519 
6535 
655i 
6567 
6583 
6599 
66i5 
663i 
6646 
6662 
6678 
6694 
6709 
6725 
6740 


5762 
5779 
5797 
58 1 5 
5832 
585o 
5867 
5885 
5902 
5920 

5937 
5954 
5972 
5989 
6006 
6023 
6o4i 
6o58 
6075 
6092 
6109 
6126 
6i43 


5765 
5782 
58oo 
58i8 
5835 
5853 
5870 
5888 
5905 
5923 
5940 
5957 
5975 
5992 
6009 
6026 
6o43 
6061 
6078 
6095 
61 12 
6129 
6i46 


576859 
5785  58 
58o3  57 
582i 
5838 


5856J54 

5873J53 

5891I52 

59o8  5i 

5926 

5943 

5960 

5978 

5995 

6012 

6029 

6o46 

6o63 


6160  6162 
617716179 
6193:6196 
621O16213 
6227  623o 
62446246 
62606263 
627716280 
6293,6296 
63io63i3 
6327  6329 
63436346 
63596362 
63766379 
63926395 
6409,6411 
64256428 
644i6444 
645716460 
6474J6476 
6490  6492 
65o665o8 
6522  6525 
6538654i 
655/6557 
65706573 
6586!6588 
66o2'66o4 
66i8|662o 
6633,6636 
6649'6652 
666516667 
668i;6683 
6696  6699 
6712  6714 
6727  6730 
6743:6746 


6098 
6n5 
6i3i 

|6i48 
6i65 

J6182 
,6199 
16216 
16232 
16249 
,6266 
6282 
,6299 
63i6 
J6332 
,6349 
6365 
638i 
6398 
64i4 
|643o 

6447 
6463 
6479 
6495 
65u 
6527 
6543 
6559 
6575 
6591 
6607 
6623 
6639 
6654 
6670 
6686 
6701 
6717 
6733 
6748 


9.996751 
6766 
6782 
6797 
6812 
6828 
6843 
6858 
6874 


i6753 
6769 
6784 
6800 
68i5 
683o 


6756 
6771 
6787 
6802 
6818 
6833 


9.996904 
6919 
6934 
6949 
6964 
6979 
6994 
7009 
7024 
7o39 
997053 
7068 
7083 
7098 
7112 
7127 
7141 
7i56 
7170 
7i85 
997199 
7214 
7228 
7242 
7257 
7271 
7285 
7299 
73i3 
7327 

9.99734i 
7355 

7369 
7383 

7397 
74u 
7425 
7439 
7452 
7466 
9.997480 
7493 
75o7 
7520 
7534 
7547 
756i 
7574 
7588 
7601 


68466848 
6861  6863 
68766879 
6894 
6906J6909 
6922  6924 
6937  6939 
6952  6954 


6967 
6982 
6997 
7011 
7026 
7041 
7o56 
7071 
7085 
7100 
71 15 
7129 
7144 
7i58 
7i73 
7187 
7202 
7216 
7230 
7245 
7259 
7273 
7287 
73oi 
73i6 
733o 
7344 
7358 
7372 
7386 

7399 
74i3 
7427 
744i 
7455 
7468 
7482 
7496 
75o9 
7523 
7536 
755o 


6969 
6984 
6999 
7014 
7029 
7044 
7o58 
7o73 
7088 
7102 
7117 
7132 
7146 
7161 
7i75 
7190 
7204 
7218 
7233 
7247 
7261 
7276 
7290 
73o4 
73i8 
7332 
7346 
736o 
7374 
7388 
7402 
7416 
7429 
7443 
7457 
7471 
7484 
7498 
75u 
7525 
7539 
7552 


75637565 
757717579 
7590  7592 
76o3j76o5 


6758 
6774 
6789 
68o5 
20 
6835 
685i 
6866 


6761 
6777 
6792 
6807 
6823 
6838 
6853 
6869 
6884 


6912 
6927 
6942 
6957 
6972 
6987 
7002 
7016 
7o3i 
7046 
7061 
7076 
7090 
7io5 
7120 
7i34 
7149 
7i63 
7178 
7192 
7206 
7221 
7235 
7249 
7264 
7278 
7292 
7306 
7320 
7334 
7348 
7362 
7376 

739° 
74o4 
74i8 
7432 
7445 
7459 
7473 
7487 
75oo 
75i4 
7527 
754i 
7554 
7568 
758i 
7594 
7608 


6914 
6929 
6944 
6959 
6974 


7004 
7019 
7o34 
7049 
7063 
7078 
7093 
7107 
7122 
7i37 


6764 
6779 
6795 
6810 
6825 
684i 
6856 
6871 
6886 
6901 
6917 
6932 

6947 
6962 
6977 
6992 
7007 
7021 
7o36 
7o5i 
7066 
7080 
7o95 
7110 
7124 
7i39 


7i5i hi54 
7166  7168 
7180  7182 
7194  7197 
7209  721 1 
7223  7226 
7238  7240 
7252  7254 
7266  7268 


7280 
7294 

73o9 
7323 

7337 
735i 
7365 

7379 
7393 

7406 
7420 
7434 
7448 
7461 
7475 
7489 

7502 
75i6 
753o 
7543 
7556 

757° 
7583 
7597 
7610 


7283 
7297 
73n 
7325 

7339 
7353 

7367 

738i 

7395 

7409 

7423 

7436 

745o 

7464 

7477 

7491 

75o5 

75i8 

7532 

7545 

7559 

737 

7585 

7599 

7612 


So 

58 

57 
56 
55 

54 
53 

52 

5i 
5o 

49 

48 

47 
46 
45 
44 
43 
42 
4i 
40 
39 
38 

37 
36 
35 

34 
33 

3  53 

3i 

3o 

9 
cS 

27 

26 

25 

24 

23 
2  2 
21 

20 

19 

l8 

J7 
16 
i5 
i'i 
1 3 
12 
1 1 
10 

9 

8 

7 
6 
5 
4 
3 
2 
I 
o 


30"  1  20" 


50"  I  40"  I  30"  I  20"  I  10" 


Co-sina  of  7  Degrees. 


Co-sine  off)  Degrees. 


P.  Tart . 


1"  2"  3'' 


4" 
1 


6' 


8"  9" 


1" 


P.  Part  J  Q 


2"  3" 
0   1 


5"  6"    7" 
1   1   2 


y" 


Logarithmic  Tangents. 


107 


I    Tangent  of  82  Degrees 


0|Jo. 852197 
3u5 
4o34 
4956 
5879 
68o4 
773i 
866o 
959i 
io.S6o524 
i458 


2395 
3333 
4274 
52 1 6 
6161 
7107 
8o56 
9006 

9959 
10.870913 
1870 

2828 
3789 

475i 
57i6 


235o 
3268 
4i88 
5no 
6o33 
6958 
7886 
88i5 
9746 
0679 
i6i4 
255i 
3490 
443 1 
5374 
6319 
7265 
8214 
9165 
118 
1072 


20"   30"   40''   50" 


25o3 
3421 

4341 

5263 
6187 
7113 
8o4i 
8970 
9902 
o835 
1770 
2708 

364? 
4588 
553i 
6476 
7423 
8372 
9324 
277 


2656  2809  2962  59 
388i  58 


3575  3728 
4495  4649 


54i7 


634i  6496 


7267 


8195  835o 
9125  9280 
..57 
0991 
1926 
2864 
38o3 
4745 
5688 
6634 
758i 
853i 
9482 
436 


1232  l39I 
2029!2l89  2349 

29883i4833o8 
3949U109U270 


4912I0073 
5877!6o38 
6683|6844|7oo6 
7652  7813  7975 
862387858947 
9596J9758  9921 


3o  10.880571  0734 


i548  1711 
2528  2691 
35o9|3673 
4493  4657 
5479  5643J58o8 
646716632  6796 
7457  762217787 


0896 

1874 
2855 
3837 

4821 


844986i5 
944419610 
10.890441J0607 


i44o 
a44i 
3444 
445o 

5458 


1606 
2608 
36i2 
46i8 
5626 


8781 
9776 
o773 
i773 
2775 
3779 
4786 
5795 


6468  6637  6806 
7481  765o  7819 
8496  866:'.  8834 
951396839852 
10.900532  0702  0873 
i554  1734  1895 
2578J2749J2920 
36o5  3776  3g47 
463348o54977 
5664  5837  6009 
669816871,7043 
7734  79<r" 


5234 
6199 
7167 
8i37 
9109 
..83 
1059 
2o38 
3oi8 
4ooi 

4985 
5972 

G96I 

7953 

8946 
9942 
0940 
1940 
2942 
3947 
49  54 
5963 
6974 
7988 
9004 
.  .22 
io43 
2066 
3091 
4i  19 
5i49 


557i 


742: 


4802 
5725 
665o  55 
7576  54 
85o5 
9436 
.368 
i3o2 
239 


.212 

n46 

2082 

3020 

3960 
4902 
5846 
6792 

7739 
8689 

9641 
.595 
i55i 
25o8 
3468 
443o 
5394 
636o 
7329 
8299 

927i  . 
246  .4o8 


3i77 
4117 
5o59 
6oo3 
6950 
7898 
8848 
9800 
.754 
1710 
2668 
3629 
4591 
5555 

6522 

7490 
846i 
9433 


1222 
2201 
3i82 
4i65 
5i5o 
6i37 
7127 
8118 
9112 
.108 
1 106 
2107 
3no 
4n5 

5l22 

6i3i 


.192 

I2l3 
2236 

3262 

4290 

5320 


6181  6353 
7216  7388 
82538426 


i385 
2364 
3345 
4329 
53i4 
63o2 
7292 
8284 
9278 
.274 
1273 

2274 
3277 
4282 
5290 

63oo  i4 
7143J73 12  1 3 

8157832612 
9173  9343  11 
.362 
1 384 
2407 
3433 
4462 
5492 
6526 
756i 
8599 


Tangent  of  83  Degrees. 


8772  894G  91 19  9292  94669639  1 
98i3 


80" 


VVS7 
50"  I 


i6i  .3341. 5o8| 


68: 

10" 


1 

2 
3 

4 
5 
6 

7 
8 

9 

id 

11 
is 
1 3 

i4 
1 5 
16 

*7 
18 

*9 

30 
21 
22 

23 

24 
25 

26 

27 

28  10 

29 

3o 
3i 

32 

33 
34 
35 
36 

'"7 
38 
39 
4o 
4i 
42 
43 
44 
45 
46 

4  7 
48 

49 
5o 
5i 

52 

53 
54'io 
55 
5C 

5? 
58 

59 


.910856 
1902 
2950 
4ooo 
5o53 
6109 
7167 
8227 
9290 


10"   20"   30" 


io3o 
2076 
3i25 
4176 
5229 
6285 
7343 
84o4 
9468 


10.920356  o534 


1424 
2495 
3568 
4644 
5722 
68o3 


1602 
673 

3747 
4823 
5902 
6984 


I2o5 
225l 

33oo 
435i 
54o5 
646 1 
7520 
858i 
9645 
0712 
1781 

2852 

3926 
5oo3 


i379 
2426 
3475 
4527 
558i 
6638 
7697 
8759 
9823 
0890 
i959 
3o3i 
4io5 
5i83 


iS53 
2600 
365o 
4702 
5757 
6814 
7874 
8936 


60826262 
7164  7345 


788780688=498430 


8973  9154 
,930062  0244 
ii54i336 
2248p43o 
33453528 
4444|4628 
554? 
6652 
7760 
8870 

9984 
.941100 
2219 
334i 
4465 
5593 
6723 


93369517 
0425  0607 
1 5i 8 1700 
2613  2796 
371 1  3894 
4812  U995 
5915  6099 
7021  7205 
8i3o83i5 
9427 
.54i 
1659 


40"   50" 


1068 

2i38 

32IO 

4=85 
5362 
644a 
7525 
861 1 
9699 
0789 
i883 
2979 
4078 
5179 
6283 

739° 
85oo 
9612 

•727 
i845 
2966 
4090 


573i 
6836 
7945 

9o56  9241 

.  169  .355 

1286  1472 

240642592  2779 

3528  37i5  390: 

4653  484i  5o28  5216 

5781  596961576346 

6912  7100  7289  747P 

7856J8o45  8234  84a4  86i3 

8992  9182  9371  9561  9751 

95oi3i  o32i  o5n  0702 

I273|i464  i654  i845 

24 1 8; 2509' 2800  2991 

3566  3757|3949!4i4i 


47164908 !5ioi  5293 
5870  6o63|6255  6448 
7027  7220  74i3  7606 
8187838085748768 
934995449738  9932 
•  96o5i5'o7io  0905  1099  1294 
i684li879'2074  227oi2465 


0892 
2o36 
3i83 
4332 
5485 
664i 
7800 
8961 
.126 


3443 
4620 
58oo 
6983 
8169 


3639 
4816 
5997 
7180 
8367 


I    Co-tangent  of  7  Degrees. 


2856i3o52  3247 
4o3i U227  4424 
5209  54o6  56o3 
6391  65886785 

7575|7773;797i 
87638961  9159 
9954J.  i5a  .35i 
97ii48[i347  i546 
2345i2545'2745 
3545|3746  3946  4i4t  4  >4? 
4749  495o  5 1 5 1  5352(5553 
5956  61 57  6359  656i  6762 
7166  7368  7r>7<>  7773  797') 


9358j9556 
.550J.749 

1746  n;45 
<;4r)  3i45 


1727 
2775 
3825 
|4878 
|5933 
6990 
8o5o 
9 1 1 3 
.178 
1246 
23i6 
3389 
4464 
5542 
6623 
7706 
8792 
9880 
0971 
2o65 
3162 
4261 
5363 
6467 
7575 
8685 
9798 
.914 

2032 

3i53j3o 
4277 

54o4 
6534 
7667 

88o3J25 
994i  24 
io8323 
2227122 

r'>  3  74;  2 1 

567819 

7993 
9i55 

.321 

i489 
2661 
3835 
5oi3 
6194,10 

7377 

8565 
9755 
•  948 
2i45 
3345 
4548 
5755 
IO964 
s'77 


40"      30"   ,    20" 


Co-tanjreiit  of  0  Degrees. 


V.I'nrt 


S  I      2"    3" 
I  16   33    49 


•J" 
6j 


SI 


6"     7"     H"     !»" 
<)S   ill  i:i()  lit. 


1'.  Part 


IS 


:i"    4"  5"    6"     7" 
".('.   7o  94   112   131 


S"     0" 

iro  168 


108 


Logarithmic    Sines. 


Sine  of  34  Degrees. 

Sine  of  85  Degrees. 

0"    i  10" 

20"  [  30" 

40" 

50" 

0"    )  10"  1  20" 

30" 

40" 

50" 

o 

9.997614 

7617 

76i9'762i 

7623 

7625 

59 

0 

9-998344  8346  8348 

835o 

8352 

8353 

59 

I 

7628 

763o 

76327634 

7636 

7639 

58 

1 

8355  8357 

8359 

836i 

8363 

8364 

58 

2 

7641 

7643 

7645,7647 

765o 

7652 

57 

2 

8366  8368 

837o 

8372 

8374 

8375 

57 

3 

7<554 

7656 

76587661 

7663 

7665 

56 

3 

83?7 

8379 

838i 

8383 

8385 

8386 

56 

4 

7667 

7669 

7672  7674 

7676 

7678 

55 

4 

8388 

8390  8392 

8394 

8395 

8397 

55 

5 

7680 

7682 

76857687 

7689 

7691 

54 

5 

8399 

84oi 

84o3 

8404 

84o6 

84o8 

54 

G 

7693 

7696 

7698  7700 

7702 

7704 

53 

6 

84io 

8412 

84i3 

84i5 

8417 

8419 

53 

7 

7706 

7709 

7711 

77i3 

77i5 

7717 

52 

7- 

8421 

8422 

8424 

8426 

8428 

843o 

52 

8 

7719 

7722 

7724 

7726 

7728 

773o 

5i 

8 

843 1 

8433 

8435 

8437 

8439 

844o 

5i 

9 

7732 

7735 

7737 

7739 

774i 

7743 

5o 

9 

8442 

8444 

8446 

8448 

8449 

845i 

5o 

IO 

9.997745 

7747 

775o 

7752 

7754 

7756 

49 

10 

9.998453 

8455 

8456 

8458 

846o 

8462 

49 

ii 

7758 

7760 

7762 

7765 

7767 

7769 

48 

11 

8464 

8465 

8467 

8469 

8471 

8472 

48 

12 

7771 

777377757777 

7780 

7782 

47 

12 

8474 

8476 

8478 

8479 

848 1 

8483 

47 

i3 

7784 

7786,77887790 
7799!78oi  7803 

7792 

7794 

46 

i3 

8485 

8487 

8488 

8490 

8492 

8494 

46 

i4 

7797 

78o5 

7807 

45 

14 

8495 

8497 

8499 

85oi 

85o2 

85o4 

45 

i5 

7809 

7811  78147816 

7818 

7820 

44 

i5 

85o6 

85o8 

8509 

85n 

85i3 

85i5 

44 

16 

7822 

78241782617828 

783o 

7833 

43 

16 

85iC 

85i8 

8520 

8522 

85^3 

8525 

43 

17 

7835 

7837  7839  7841 

7843 

7845 

42 

17 

8527 

8529 

853o 

8532 

8534 

8535 

4a 

18 

7847 

78497852  7854 

7856 

7858 

4i 

18 

8537 

8539 

854i 

8542 

8544 

8546 

4i 

J9 

7860 

7862  78647866 

7868 

7870 

4o 

l9 

8548 

8549 

855i 

8553 

8554 

8556 

4o 

20 

9.997872 

7875i7877,7879 

7881 

7883 

39 

20 

9-998558 

856o 

856i 

8563 

8565 

8566 

39 

21 

7885 

7887:788917891 

7893 

7895 

38 

21 

8568 

8570 

8572 

8573 

8575 

8577 

38 

22 

7897 

7900  7902  7904  7906  7908 

37 

22 

8578 

858o 

8582 

8584 

8585 

8587 

37 

23 

7910 

7912  791417916 

7918 

7920 

36 

23 

8589 

859o 

8592 

8594 

8595 

8597 

36 

24 

7922 

792479267929 

793i 

7933 

35 

24 

8599 

8601 

8602 

8604 

8606 

8607 

35 

25 

7935 

793779397941 

7943 

7945 

34 

25 

8609 

8611 

8612 

8614 

8616 

8617 

34 

26 

7947 

7949,7951  7953 

7955 

7957 

33 

26 

8619 

8621 

8622 

8624 

8626 

8627 

33 

27 

7959 

7961  7963,7965 

7967 

7970 

32 

27 

8629 

863i 

8633 

8634 

8636 

8638 

32 

28 

7972 

79747976,79787980 

7982 

3i 

28 

863g 

864i 

8643 

8644 

8646 

8648 

3i 

29 

7984 

7986  7988|7990j7992  7994 

3o 

29 

8649 

865i 

8653 

8654 

8656 

8657 

3o 

3o 

9.997996 

7998  8000  8002  8oo4  8006 

29 

3o 

9.998659 

8661 

8662 

8664 

8666 

8667 

29 

3i 

8008 

8010  8012  8oi4  8oi6|8oi8 

28 

3i 

8669 

8671 

8672 

8674 

8676 

8677 

28 

32 

8020 

8022  8024  8026 

8028,8030 

27 

32 

8679 

8681 

8682 

8684 

8686 

8687 

27 

33 

8o32 

8o34  8o36  8o38 

8o4o8o42 

26 

33 

8689 

8690 

8692 

8694 

8695 

8697 

26 

34 

8o44 

8o46  8o48  8o5o 

8o52'8o54 

25 

34 

8699 

8700 

8702 

8704 

87o5 

8707 

25 

35 

8o56 

8o58  8060  8062 

8064*8066 

24 

35 

8708 

8710 

8712 

87i3 

87i5 

8717 

24 

36 

8068 

8070  8072  8074 

8o76!8o78 

23 

36 

8718 

8720 

8721 

8723 

8725 

8726 

23 

37 

8080 

8082  8o84!8o86  80888090  22 

37 

8728 

8729 

873i 

8733 

8734 

8736 

22 

38 

8092 

8094  8096  8o98'8ioo'8io2  21 

38 

8738 

8739 

874i 

8742 

8744 

8746 

21 

39 

8104 

8io68io8;8iio!8ii2'8ii42o 

39 

8747 

8749 

8750 

8752 

8754 

8755 

20 

4o 

9.998116 

8n88i20!8i228i248i26  19 

4o 

9.998757 

8758 

8760 

8762 

8763 

8765 

J9 

4i 

8128 

8i3o8i3i  8i338i358i37 

18 

4i 

8766 

8768 

8769 

8771 

8773 

8774 

18 

42 

8i39 

8i4i  8i43 8i45 81478149 

J7 

42 

8776 

8777 

8779 

8781 

8782 

8784 

17 

43 

8i5i 

8I53.8i558i57i8i598i6i 

16 

43 

8785 

8787 

8788 

8790 

8792 

8793 

16 

44 

8i63 

8i658i6718i68!8i7o8i72 

i5 

44 

8795 

8796 

8798 

8799 

8801 

88o3 

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45 

8i74 

8i768i78J8i8o8i82!8i84 

i4 

45 

88o4 

8806 

8807 

8809 

8810 

8812 

14 

46 

8186 

8188  8190J8192J8194  8195 

i3 

46 

88i3 

88i5 

8817 

8818 

8820 

8821 

i3 

47 

8197 

8199  8201  82o3i82o5  8207 

12 

47 

8823 

8824 

8826 

8827 

8829 

883i 

12 

48 

8209 

S2ii;82i382i582i782i8 

1 1 

48 

8832 

8834 

8835 

8837 

8838 

884o 

11 

49 

8220 

8222  8224822682288230 

IO 

49 

884i 

8843 

8844 

8846 

8848 

8849 

10 

5o 

9.998232 

82348236823882398241 

9 

5o 

9.998851 

8852 

8854 

8855 

8857 

8858 

9 

5i 

8243 

8245824782498251,8253 

8 

5i 

8860 

8861 

8863 

8864 

8866 

8867 

8 

52 

8255 

82578258:826082628264 

7 

52 

8869 

8870 

8872 

8873 

8875 

8877 

7 

53 

8266 

826882708272182738275 

6 

53 

8878 

88808881 

8883 

8884 

8886 

6 

54 

8277 

82798281  828382858287 

5 

54 

8887 

88898890 

8892 

8893 

8895 

5 

55 

8289 

8290|8292;8294  8296  8298 

4 

55 

8896 

88988899 

8901 

8902  8904 

4 

56 

83oo 

83o2  83o3  83o5  83o783o9 

3 

56 

8905  8907  8908  8910 

8911  89i3 

3 

57 

83n 

83i3;83i5'83i6;83i8  832o 

2 

57 

8914  8916  89178919 

8920,8922 

2 

58 

8322  8324  8326  83288329  833i  1 

58 

89238925  89268927  8929^8930 

1 

59 

8333  8335  8337'8339!834i  8342  0 

59 

8932  8933  89358936:89388939 

0 

GO"    |  50"  |  40"  |  30"  |  20"   10"  |  ^ 

1 

60"    ,  50"   40"  I  30"  1  20"  |  10" 

c 

Co-sine  of  5  Degrees.      § 

Co-sine  of  4  Degrees. 

IS 

P. 
L 

p  .$  1"  2"  3"  4"  5"  6"  7"    8"  9"  II  „ 
lan\   0   0   1   1   1   1   1   2   2  |j  1- 

p  A  I"    2"  3"  4"  5"  6"  7"   8"  9" 
lart\   0   0   0   1   1   1   1  '  1   1 

LOGARITHMIC      TANGENTS. 


109 


0 

Tangent  of  84  Degrees. 

0 

Tangent  of  85  Desrreos. 

0" 

10" 

20" 

30" 

40" 

50" 

0"     |  10" 

20" 

30"  1  40"  |  50" 

ic. 978380 

8582 

8785 

8988 

9191 

9394  59 

11  .o58o48  8291 

8533 

8776  901919262 

59 

I 

q597 

9800 

...3 

.206 

•  4io 

.6i3 

58 

I 

95o6  9749 

9993 

.236 

.480  .724 

58 

2 

10.980817 

1021 

1224 

1428 

i632 

i836 

>7 

2 

11 .060968 

1212 

i456 

1701 

1945  2190 

57 

3 

204l 

2245 

2449 

2654 

2858 

3o63 

56 

3 

2435 

2680 

2925 

3170 

34i6366i 

56 

4 

3268 

3472 

3677 

3882 

4087 

4293 

55 

4 

3907 

4i53 

4399 

4645 

4891  5i38 

55 

5 

4498 

4703 

4909 

5n4 

5320 

5526 

54 

5 

5384 

563i 

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50"  |  40"  I  30*  1  20"  1  10' 

| 

Co-tangent  of  5  Degrees. 

Co-tangent  of  4  Degrees. 

P 

Part  J  l"  2"   3"  4"  5"   (J"   7"   8"   9" 
l*ri)  22  41  GG  88  110  132  154  177  199 

„  p   (  1"  2"  3"  4"  5"  6"  7"  8"  9" 
1  .  I  urt  ^  2.  54  gl  ,08  13-  1(]2  ]g8  „15  242 

110 


^Logarithmic    Sines. 


Sine  of  86  Degrees. 


40"       5C 


Sine  of  87  Degrees. 


10"       20"       30"       49'       5C 


o 
I 

2 

3 

4 
5 

6 

7 

8 

9 

IO 

II 

12 

i3 

i4 

1 5 

1 6 

17 
18 

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20 

21 

22 

23 

«*4 

26 

27 

25 

29 

3o 
3i 

32 

33 
34 
35 
36 

3? 

38 
39 
4o 

4i 
4'= 
43 
44 
45 
46 

47 

45 

49 
5o 
5i 

52 

53 
54 
55 
56 

57 
58 
59 


9.998941 
8950 


8967 
8976 


8993 
9002 
9010 
9019 
999027 
9036 
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9069 
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9991 10 
9118 
9126 
9134 
9142 
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9i58 
9166 
9174 
9181 

9.999189 
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9212 
9220 
9227 
9235 
9242 
9250 
9257 

9.999265 
9272 
9279 
9287 
9294 
9301 
9308 
931 5 
9322 
9329 

9.999336 
9343 
935o 

9357 
9364 
937i 
9378 
9384 
9391 
9398 


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8951  895389548955 
89608961  89638964 
8969'897o  8971  8973 
8977  8979  8980  8982 
8986,898789898990 
899589968997  8999 
9003  90059006  9007 
9012  9013  9015  9016 
9020  9022  9023  9024 
9029  9030  9032  9033 
9037  9039  9040 J904 1 
9046"  9047  9048 19050 
9054  9055  9057  9058 
9062  9064  9065  9066 
907^9072  9073  9075 
9079  9080  9082  9083 
9087  90889090  9091 
9095  9097  9098  9099 


8957 
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8974 


9103  9ip5  9106 
9111  9113J9114 
9120  912119122 
9128  9129  9130 
91 36  91 3791 38 
9143  9145,9146 
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9159  9161  9162 
9167  9168,9170 
9175  9176^178 
gi83  9i84:9i85 
9190  919219193 
9198  9199  9201 
9206  92079208 
9213  9215  9216 
1  9222  9224 
9229  9230  9231 
9236  9237  9239 
9244  9245  9246 
9251  9252  9254 
9258  9260  9261 
9266  9267  9268 
9273  92749276 
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9288  9289  9290 
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9316  9318  9319 
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9l57 
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9372  9373 
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50" 


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9374 
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91879188 
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92179219 

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9348:9349 
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9362  9363 
9369  9370 

9375  9377 
9382  9383 

9389  9390 
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9402  94o3 


20"   10" 


Co-sine  of  3  Decrees. 


3 
4 
5 
6 

7 
8 

9 

id 

1 1 
12 
1 3 
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33 

34 
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36 

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39 
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43 

44 
45 
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47 
45 

49 
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52 

53 

54 
55 
50 

57 
58 
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9470 
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9665 
9670 
9675 
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9477 
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9560 
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9614 
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965i 
9656 
9661 
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9671 
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9690 
9695 
9700 
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9599 
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9720  9721 

9725*9726 

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50"  I  40"  I  30"  I  20" 


Co-sine  of  2  Degrees. 


59 

58 

57 
56 
55 
54 
53 
52 
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49 

48 

47 
46 
45 
44 
43 
42 
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39 
38 

37 
36 
35 

34 
33 

32 

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29 

25 

27 
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l\  Tart 


1"  2"  3"  4" 
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6"  7"  8"  9" 
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6"    7"    8"    9" 
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J 

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r  A  N  O  E  K  T  S. 

111 

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9 

Tangent  of  86  Degrees. 

i 

Tangent  of  87  Degrees. 

0" 

10" 

20" 

30" 

40"  I  50" 

0" 

10"  1  20" 

30" 

40" 

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0 

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112 


Logarithmic    Sines. 


Sine  of  88  Degrees. 

i 

Sine  of  89  Degrees. 

1 

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0 

60"    |  50" 

40"   30" 

20" 

10" 

3 

60" 

50"  J  40" 

30"  |  20" 

10" 

a 

Co-sine  of  1  Degree. 

Co-sine  of  0  Degree. 

3 

r. 

p  A  1"  2"  3"  4"  5"  6"  7"    8"  9" 
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P. 

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Logarithmic    Tangents. 


113 


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Tangent  of  88  Degrees. 

r.  Tart 
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0" 

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612771 

6 1 3636 

6i45o2 

615370 

616240 

23 

86.7 

3? 

617111 

617985 

618860 

619737 

620615 

621496 

22 

87.8 

38 

622378 

623262 

624147 

625o35 

625924 

626810 

21 

88.8 

39 

627708 

628603 

629500 

630399 

631299 

632201 

20 

89.9 

4o 

n.633io5 

11 .634oi2 

1 1 .634919 

n.635829 

1 1. 636741 

1 1 .637655 

'9 

91. 1 

4i 

63857o 

639488 

640407 

64i329 

642252 

643177 

18 

93.1 

42 

644io5 

645o34 

645965 

646899 

647834 

648771 

17 

93.4 

43 

64971 1 

65o652 

65 1 595 

65254i 

653488 

654438 

16 

94.6 

44 

655390 

656343 

657299 

658s57 

659217 

660179 

i5 

95.9 

45 

66n44 

6621 10 

663079 

664o5o 

665023 

665998 

i4 

97.2 

46 

666975 

667955 

668936 

669920 

670907 

671895 

i3 

98.5 

47 

672886 

673879 

674874 

675871 

676871 

677873 

12 

99.8 

48 

678878 

679885 

680894 

681905 

682919 

683935 

1 1 

101 .3 

49 

684954 

685975 

686998 

688024 

689o52 

690083 

10 

102.7 

5o 

1 1 .691 1 16 

11 .692151 

11 .693189 

: 1 .694230 

11 .695273 

11. 696318 

9 

104.3 

5 1 

697366 

698417 

699470 

700526 

7oi584 

702645 

8 

105.7 

52 

703708 

704774 

7o5843 

706914 

707988 

709065 

7 

107.3 

53 

710144 

71 1226 

'7 1 2  3 1 1 

713398 

7i4488 

7 1 558 1 

6 

108.9 
no. 5 

54 

^16677 

717775 

718876 

719980 

721087 

722196 

5 

55 

723309 

724424 

725542 

726663 

727787 

738914 

4 

113  3 

56 

73oo44 

731176 

73s3i2 

73345i 

734592 

735737 

3 

i  i4.o 

5  7 

736885 

738o35 

739189 

74o346 

74i5o6 

742669 

2 

n5.8 

58 

743835 

745oo4 

746177 

747352 

74853i 

749713 

1 

117. 7 

59 

750898 

752087 

753279 

754474 

755672 

756874 

0 

JL1!:!- 

60' 

30" 

40" 

30" 

of  1  Degree 

SO" 

10" 

. 

i 

< 

Uo-tangent 

5 

II 


114 


Auxiliary    Table   for   Sines,   t£c. 


1 

E 

3 

s 

0  Degree. 

4 

§ 
0 

| 

1  Degree 

log.  sin.  A — 
log.  A''. 

log.  tan.  A — 

log.  cot  A+ 

§ 

log.  sin.  A — 
log.  A". 

log.  tan.  A — 

iOg.  cot  A  +■ 
log.  A". 

m 

S 

log.  A". 

log.  A". 

03 

3 

log.  A". 

o 

0 

4.685575 

4.685575 

l5.3l4425 

60 

36oo 

0 

4.685553  4.6856i9 

i5.3i438i 

60 

60 

1 

575 

575 

425 

59 

366o 

I 

552 

620 

38o 

59 

120 

2 

575 

575 

425 

58 

3720 

2 

55i 

622 

378 

58 

180 

3 

575 

575 

425 

5? 

3780 

3 

55i     623 

377 

57 

24o 

4 

575 

575 

425 

56 

384o 

4 

55o 

625 

375 

56 

3oo 

5 

575 

575 

425 

55 

3900 

5 

549 

627 

373 

55 

36o 

6 

575 

575 

425 

54 

3960 

6 

548 

628 

372 

54 

420 

7 

575 

575 

4a5i53 

4020 

7 

547 

63o 

37o 

53 

48o 

8 

574 

576 

424 

52 

4o8o 

8 

547 

632 

368 

5a 

54o 

9 

5  74 

576 

4a4 

5i 

4i4o 

9 

546 

633 

367 

5i 

600 

10 

4.685574 

4.685576 

i5.3i4424 

5o 

4200 

10 

4.685545 

4.685635 

i5.3i4365 

5o 

660 

11 

574 

576 

424 

49 

4260 

1 1 

544 

637 

363 

49 

720 

12 

5  74 

577 

423 

48 

4320 

12 

543 

638 

362 

48 

780 

1 3 

5  74 

577 

423 

47 

438o 

i3 

542 

64o 

36o 

47 

84o 

i4 

5  74 

577 

423 

46 

444o 

i4 

54i 

642 

358 

46 

900 

i5 

573 

578 

422 

45 

45oo 

i5 

54o 

644 

356 

45 

960 

16 

573 

578 

422 

44 

456o 

16 

539 

646 

354 

44 

1020 

*7 

573 

578 

422 

43 

4620 

17 

539 

647 

353 

43 

1080 

18 

573 

579 

421 

42 

468o 

lb 

538 

64g 

35i 

42 

n4o 

J9 

573 

579 

421 

4i 

474o 

:9 

537 

65i 

349 

4i 

1200 

20 

4.685572 

4.68558o 

i5.3i442o 

4o 

48oo 

20 

4.685536 

4.685653 

i5. 3i4347 

4o 

1260 

21 

572 

58o 

420 

39 

486o 

21 

535 

655 

345 

39 

l320 

22 

572 

58i 

419 

38 

4920 

22 

534 

657 

343 

38 

i38o 

23 

572 

58i 

419 

37 

4980 

23 

533 

659 

34i 

37 

i44o 

24 

57i 

582 

4i8 

36 

5o4o 

24 

532 

661 

339 

36 

i5oo 

25 

57i 

583 

417 

35 

5 1 00 

2  5 

53i 

663 

337 

35 

i56o 

26 

57i 

583 

417 

34 

5 1 60 

26 

53o 

665 

335 

34 

1620127 

570 

584 

416 

33 

5220 

27 

529 

668 

332 

33 

168028 

570 

584 

4i6 

32 

5280 

28 

527 

670 

33o|32 

174029 

570 

585 

4i5 

3i 

534o 

29 

526 

672 

328 

3i 

1800  3o 

4.685569 

4.685586 

i5.3i44i4 

3o 

54oo 

3o4- 685525 

4.685674 

i5.3i4326 

3o 

i86o3i 

569 

587 

4i3 

29 

546o 

3i 

524 

676 

324 

29 

1920 

32 

56g 

587 

4i3 

28 

5520 

32 

523 

679 

321 

28 

1980 

33 

568 

588 

412.27 

558o 

33 

522 

681 

319 

27 

2o4o 

34 

568 

589 

4n 

26 

564o 

34 

521 

683 

3i7 

26 

2100  35 

567 

590 

4io 

25 

5700 

35 

520 

685 

3i5 

25 

2160  36 

567 

591 

409 

24 

5760 

36 

5i8 

688 

3l2 

24 

2220 

37 

566 

592 

4o8 

23 

5820 

37 

517 

690 

3io 

23 

2280 

38 

566 

593 

407 

22 

588o 

38 

5i6 

693 

307 

22 

234o 

39 

566 

593 

407 

21 

5940 

39 

5i5 

695 

3o5 

21 

2400 

4o 

4.685565 

4.685594 

i5.3i44o6 

20 

6000 

4o 

4.6855i4 

4.685697 

i5.3i43o3 

20 

2460 

4i 

565 

595 

4o5 

*9 

6060 

4i 

5l2 

700 

3  00 

!9 

2520 

42 

564 

596 

4o4 

18 

6120 

42 

5n 

702 

298 

18 

258o43 

564 

598 

4o2 

17 

6180 

43 

5io 

7o5 

295 

17 

2640  44 

563 

599 

4oi 

16 

6240 

44 

509 

707 

293 

16 

2700 

45 

562 

600 

4oo 

i5 

63oo 

45 

507 

710 

290 

15 

2760 

40 

562 

601 

399 

i4 

636o 

46 

5o6 

7i3 

287 

i4 

2820 

47 

56i 

602 

398 

i3 

6420 

47 

5o5 

7i5 

285 

i3 

2880 

48 

56i 

6o3 

397 

12 

648o 

48 

5o3 

718 

282 

12 

2940 

49 

56o 

6o4 

396 

11 

654o 

49 

502 

720 

280 

11 

3ooo 

5o 

4.68556o 

4.6856o5 

15.314395 

10 

6600 

5o 

4.6855oi 

4.685723 

i5. 314277 

10 

3o6o 

5i 

559 

607 

393 

9 

6660 

5i 

499 

726 

274 

9 

3l20 

52 

558 

608 

392 

8 

6720 

52l    498 

729 

271 

8 

3i8o 

53 

558 

609 

391 

7 

6780 

53 

497 

73i 

269 

7l 

324o  54 

557 

611 

389 

6 

684o 

54 

495     734 

266 

6 

33oo 

55 

556 

612 

388 

5 

6900 

55 

494 

737 

263 

I 

336o 

56 

556 

6i3 

387 

4 

6960 

56 

492 

740 

260 

4 

3420 

57 

555 

6i5 

385 

3 

7020 

5? 

491;     743 

257 

3 

348o 

58 

554 

616 

384 

2 

7080 

53 

490J     745 

255 

2 

354o 

59 

554 

618 

382 

1 

7140 

59 

488     748 

252 

I 

log.  cos.  A — 

log.  cot  A — 

log.  tan.  A-f. 

<« 

log.  cos.  A — log.  cot  A — 

log.  tan.  A+ 

OB 

log.  c.  A". 

log.  c.  A". 

log.  c.  A." 

2 

.a 
2 

log.  c.  A",  log.  c.  A". 

log.  c.  A''. 

■8 

3 
.3 
3 

89  Degrees. 

88  Degrees. 

Logarithmic    Tangents. 


115 


!  , 

! 

Tangent  of  89  Degrees 

1 

1 

P.  Part 
tol". 

s 

0" 

10" 

20" 

30" 

40" 

50" 

o 

11 .758079 

11.759287 

II .760498 

11. 761714 

11 .762932 

II .764l54 

59 

121 .7 

I 

765379 

766608 

767840 

769076 

77o3i5 

77i558 

58 

123.8 

2 

772805 

774o55 

775308 

776566 

777826 

779091 

57 

125.9 

3 

780359 

781631 

782907 

784186 

785470 

786757 

56 

128. 1 

4 

788047 

789342 

790641 

791943 

79325o 

79456o 

55 

i3o.4 

5 

795874 

797192 

7985i5 

799841 

801171 

8o25o6 

54 

i32.8 

6 

8o3844 

805187 

8o6534 

8o7885 

809240 

810600 

53 

135.3 

7 

811964 

8i3332 

814704 

816081 

817462 

818847 

52 

i37.9 

8 

820237 

821632 

823o3i 

824434 

8a5842 

827255 

5i 

i4o.6 

9 

828672 

830094 

83i520 

832951 

834387 

835828 

5o 

143.4 

IO 

11.837273 

11.838724 

11. 840179 

11. 841639 

n.843io4 

11.844574 

49 

i46.a 

ii 

846o48 

847528 

849013 

85o5o3 

851999 

853499 

48 

149.3 

12 

855oo4 

8565i5 

858o3i 

859553 

861079 

862611 

47 

152.4 

i3 

864i49 

865692 

867240 

868794 

870354 

871919 

46 

i55.7 

i4 

873490 

875067 

876649 

878237 

879831 

88i43i 

45 

159. 1 

i5 

883o37 

884648 

886266 

887890 

889519 

891155 

44 

162.7 

16 

892797 

894446 

896100 

897761 

899429 

901103 

43 

166.4 

*7 

902783 

904470 

906163 

907863 

909569 

911283 

42 

170.3 

18 

9i3oo3 

914730 

916464 

918205 

919953 

921707 

4i 

174.4 

*9 

923469 

925239 

927015 

928799 

930590 

932388 

4o 

178.7 

20 

11 .934194 

11 .936008 

11 .937829 

11.939658 

11. 941494 

11.943338 

39 

i83.3 

21 

945191 

947051 

948919 

950795 

952679 

954572 

38 

188.0 

22 

956473 

958382 

960299 

962225 

964160 

966103 

37 

193.0 

23 

968o55 

970016 

971986 

973965 

975952 

977949 

36 

198.3 

24 

979956 

981971 

983996 

986030 

988074 

990128 

35 

203.9 

25 

992191 

994264 

996347 

998440 

1 2.ooo543 

12.002657 

34 

209.8 

20 

12.004781 

12.006915 

12.009060 

I2,OII2l5 

oi3382 

oi5559 

33 

216.2 

27 

017747 

019946 

022l56 

024378 

02661 1 

028855 

32 

222  7 

28 

o3im 

033379 

o35659 

o3795l 

o4o255 

042572 

3i 

Z29.3 

29 

044900 

047242 

049596 

o5l963 

o54342 

056735 

3o 

237.3 

3o 

12.059142 

i2.o6i56i 

12.063994 

I  2. o6644l 

12.068902 

12.071377 

29 

245  4 

3i 

073866 

076369 

078887 

o8l4l9 

083966 

086529 

28 

254.0 

32 

089106 

091699 

094308 

O96932 

099572 

102228 

27 

263.2 

33 

104901 

107590 

110296 

113019 

115760 

118517 

26 

273.2 

34 

121292 

i24o85 

126896 

129726 

132574 

1 3544o 

25 

283.9 

35 

i38326 

l4l23l 

i44i56 

147100 

i5oo65 

i53o5o 

24 

295.4 

36 

i56o56 

159082 

i62i3o 

165199 

168290 

171404 

23 

3o8.o 

37 

174540 

177698 

180880 

i84o85 

.i873i4 

190567 

22 

321.7 

38 

193845 

197148 

200476 

2o383o 

207210 

2 1 06 1 6 

21 

336.7  • 

39 

214049 

217510 

220998 

2245i5 

228060 

23i635 

20 

353.1 

4o 

12.235239 

12.238873 

12.242538 

12.246235 

12. 249963 

i2.253723 

*9 

371  .a 

4i 

257516 

261342 

2652o3 

269098 

273028 

276995 

18 

391.3 

42 

280997 

285o37 

289115 

293232 

297388 

3oi584 

17 

4i3.6 

43 

3o582i 

3ioioo 

3l4422 

318787 

323ig6 

327650 

16 

438.7 

44 

332i5i 

336698 

341294 

345939 

35o634 

35538i 

i5 

467.0 

45 

36oi8o 

365o32 

369940 

374903 

379924 

385oo4 

i4 

499.2 

46 

390143 

395345 

400609 

4o593S 

4n333 

416796 

i3 

536.2 

47 

422328 

427932 

433610 

439362 

445192 

45noo 

12 

579.1 

48 

457091 

463i65 

469325 

475574 

48 19 1 5 

488349 

11 

629.4 

49 

494880 

5oi5io 

508244 

5i5o83 

522032 

529094 

10 

689.4 

5o 

12.536273 

12.543572 

12.550996 

12.558549 

12.566236 

12.574061 

9 

5i 

582o3o 

590148 

598421 

6o6854 

6i5454 

624228 

8 

52 

633i83 

642327 

651667 

661212 

670972 

680956 

7 

53 

691175 

701641 

712365 

723360 

73464i 

746223 

6 

54 

758122 

770357 

782946 

79591 1 

809275 

823o63 

5 

55 

*8373o4 

852027 

867267 

883o6i 

899452 

9i6485 

4 

56 

934214 

952697 

972002 

99220C 

i3.oi3395 

i3. 035671 

3 

■r>7 

13. o59i53 

13.083976 

1 3 . 1 io3o5 

i3. 138334 

168297 

20048a 

a 

58 

235244 

273032 

3i4425 

36oi83 

4u335 

469327 

1 

59 

536274 

6i5455 

712365 

8373o4 

14.013395 

i4.3i4425 

0 

00" 

50" 

40" 

30" 

30" 

10" 

5 

X 



— . 

( 

^o-tangent 

)f  0  Degree 

116 


Natural    Sines. 


_jfi_ 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

O 

000000 

017452 

034899 

o52336 

069756 

087156 

104528 

121869 

139173 

1 56434 

60 

I 

0291 

7743 

5i9o 

2626 

070047 

7446 

4818 

2i58 

9461 

G722 

59 

o 

o582 

8o34 

548i 

2917 

0337 

7735 

5107 

2447 

9749 

7009 

58 

3 

o873 

8325 

5772 

3207 

0627 

8025 

5396 

2735 

140037 

7296 

57 

4 

1164 

8616 

6062 

3498 

0917 

83i5 

5686 

3o24 

o325 

7584 

56 

5 

i454 

8907 

6353 

3788 

1207 

86o5 

5975 

33i3 

o6i3 

7871 

55 

6 

1745 

9X97 

6644 

4079 

1497 

8894 

6264 

36oi 

0901 

8i58 

54 

7 

2o36 

9488 

6934 

4369 

1788 

9184 

6553 

3890 

1189 

8445 

53 

8 

2327 

9779 

7225 

466o 

2078 

9474 

6843 

4179 

1477 

8732 

52 

9 

2618 

020070 

75i6 

495o 

2368 

9763 

7182 

4467 

1765 

9020 

5i 

IO 

002909 

o2o36i 

037806 

o5524i 

072658 

090053 

107421 

124756 

i42o53 

159307 

5o 

ii 

3200 

o652 

8097 

553i 

2948 

o343 

7710 

5o45 

234i 

9594 

49 

12 

3491 

0942 

8388 

5822 

3238 

o633 

7999 

5333 

2629 

9881 

48 

i3 

3782 

1233 

8678 

6112 

3528 

0922 

8289 

5622 

2917 

160168 

47 

i4 

4072 

i524 

8969 

6402 

38i8 

'  1212 

8578 

5910 

32o5 

o455 

46 

i5 

4363 

i8i5 

9260 

6693 

4io8 

i5o2 

8867 

6199 

3493 

0743 

45 

16 

4654 

2106 

955o 

6983 

4399 

1791 

9i56 

6488 

3780 

io3o 

44  . 

17 

4945 

2397 

984i 

7274 

4689 

2081 

9445 

6776 

4o68 

1317 

43 

18 

5236 

2687 

o4oi32 

7564 

4979 

2371 

9734 

7065 

4356 

1604 

42 

J9 

5527 

2978 

0422 

7854 

5269 

2660 

II0023 

7353 

4644 

1891 

4i 

20 

oo58i8 

023269 

040713 

o58i45 

075559 

092950 

iio3i3 

127642 

144932 

162178 

4o 

21 

6109 

356o 

1004 

8435 

5849 

3239 

0602 

7930 

5220 

2465;39 

22 

6399 

385i 

1294 

8726 

6i39 

3529 

0891 

8219 

5507 

2752 

38 

23 

6690 

4i4i 

i585 

9016 

6429 

3819 

1180 

8507 

5795 

3o39  37 

24 

6981 

4432 

1876 

9306 

6719 

4io8 

1469 

8796 

6o83 

3326  36 

25 

7272 

4723 

2166 

9597 

7009 

4398 

i758 

9084 

6371 

36i3 

35 

2fi 

7563 

5oi4 

2457 

9887 

7299 

4687 

2047 

9373 

6659 

3900 

34 

ay 

7354 

53o5 

2748 

060177 

7589 

4977 

2336 

9661 

6946 

4187 

33 

28 

8i45 

5595 

3o38 

o468 

7879 

5267 

2625 

9949 

7234 

4474 

32 

29 

8436 

5886 

3329 

o758 

8169 

5556 

2914 

i3o238 

7522 

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Natural  Co-sines. 

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85   |  84° 

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A 

7. 

Natural  Co-tanpe 

nts. 

to  1-4.85 

4.85 

4.86 

4.87 

4.88 

4.89 

4.91 

4.93 

4.96 

4.98 



118 


Natural    Sines. 


rv 
1 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

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19° 

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1 

79° 

78° 

77° 

76° 

75° 

740 

73°  |  72° 

71°  1  70° 

, 

Natural  Co-sines. 

S, 
1 

P.P.  , 

to  l".  4. 77 

4.75 

4.73 

4.71 

4.69 

4.67 

4.65 

4.62 

4.60 

4.57 

—  — , 

Natural    Tangents. 


119 


u 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18°  |  19° 

o 

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212557 

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2 

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5563 

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3 

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4 

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6207 

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5 

7827 

5890 

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0892   3865 

9 

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488. 

5954'   7373   9159 

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Natural  Co-tanpenis. 

P.  P.  r  co 

tor  5.53 

5.6o 

5.68 

5.76 

5.85 

5.95 

6.00  '  6.16  !  6.28 
1      1 

6.4o 

122 


Natural    Sines. 


[t 

30= 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

r~" 

o 

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9434 

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2047 

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5537 

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9675 

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8256 

2280 

6120 

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58 

3 

0756 

5786 

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5371 

9916 

4291 

8491 

25l2 

6349 

9998 

57 

4 

1007 

6o35 

0906 

56i5 

56oi57 

4529 

8726 

2  744 

6578 

630224 

56 

5 

1259 

6284 

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5858 

0398 

4767 

8961 

2976 

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55 

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6533 

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6102 

0639 

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9196 

3208 

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1762 

6782 

1645 

6346 

0880 

5243 

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7265 

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6589 

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548i 

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9 

2266 

7280 

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517529 

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2769 

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3020 

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2930 

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2623 

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57 

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3907   8469 

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3 1 00 

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2 

59 

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5432 

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1 

59° 

58°    I  57° 

56° 

55°    |  54°  |  53° 

52°  | 

51° 

50° 

Natural  Co-sines. 

[to£>i8 

4.i3 

4.09 

4.o4 

4.00 

3.95 

3.90 

3.85  1 

3.8o 

3.74 

— 

Natural.    Tangents. 


123 


i 

30° 

31° 

32° 

33° 

34° 

35° 

36°   37° 

38° 

39° 

o 

577350 

600861 

624869 

649408 

674509 

700208 

726543 

753554 

781286 

809784 

60 

I 

7738 

1257 

5274 

9821 

4932 

064 1 

6987 

4oio 

1754 

810266 

59 

2 

8126 

i653 

5679 

65o235 

5355 

1075 

7432 

4467 

2223 

0748 

58 

3 

85i4 

2049 

6o83 

0649 

5779 

1 509 

7877 

4923 

2692 

I23o 

57 

4 

8903 

2445 

6488 

io63 

6203 

1943 

8322 

538o 

3i6i 

1712 

56 

5 

9291 

2842 

6894 

i477 

6627 

2377 

8767 

5837 

363i 

2195 

55 

6 

9680 

3239 

7299 

1892 

7o5i 

2812 

9213 

6294 

4ioo 

2678 

54 

7 

58oo68 

3635 

7704 

23o6 

7475 

3246 

9658 

675i 

4570 

3i6i 

53 

8 

0457 

4o32 

8110 

2721 

7900 

368i 

73oio4 

7209 

5o4o 

3644 

52 

9 

o846 

4429 

85i6 

3i36 

8324 

4n6 

o55o 

7667 

55io 

4128 

5i 

IO 

58i235 

604827 

628921 

65355i 

678749 

7o455i 

730996 

758i25 

785981 

814612 

5o 

ii 

1625 

5224 

9327 

3966 

9174 

4987 

i443 

8583 

645 1 

5096 

49 

12 

20l4 

5622 

9734 

4382 

9599 

5422 

889 

9041 

6922 

558o 

48 

i3 

24o3 

6019 

63oi4o 

4797 

680025 

5858 

2336 

95oo 

7394 

6o65 

47 

i4 

2793 

6417 

o546 

52i3 

o45o 

6294 

2783 

9959 

7865 

6549 

46 

i5 

3i83 

68i5 

0953 

5629 

0876 

6730 

323o 

760418 

8336 

7o34 

45 

16 

3573 

7213 

i36o 

6o45 

i3o2 

7166 

3678 

0877 

8808 

75i9 

44 

17 

3963 

761 1 

1767 

646 1 

1728 

7603 

4i25 

i336 

9280 

8oo5 

43 

18 

4353 

8010 

2174 

6877 

2  I  54 

8039 

4573 

1796 

9752 

8491 

42 

*9 

4743 

84o8 

258i 

7294 

258o 

8476 

5o2i 

2256 

790225 

8976 

4i 

20 

585i34 

608807 

632988 

657710 

683007 

708913 

735469 

762716 

790697 

819463 

4o 

21 

5524 

9205 

3396 

8127 

3433 

935o 

5917 

3i76 

1170 

9949 

39 

22 

5915 

9604 

38o4 

8544 

386o 

9788 

6366 

3636 

i643 

820435 

38 

23 

63o6 

6iooo3 

4211 

8961 

4287 

710225 

68i5 

4097 

2117 

0922 

37 

24 

6697 

o4o3 

4619 

9379 

4714 

o663 

7264 

4558 

2590 

1409 

36 

25 

7088 

0802 

5027 

9796 

5i42 

IIOI 

77i3 

5019 

3o64 

1897 

35 

26 

7479 

1201 

5436 

660214 

5569 

i539 

8162 

548o 

3538 

2384 

34 

27 

7870 

1601 

5844 

o63i 

5997 

1977 

8611 

594i 

40I2 

287a 

33 

28 

8262 

2001 

6253 

1049 

6425 

24l6 

9061 

64o3 

4486 

336o 

32 

29 

8653 

2401 

6661 

1467 

6853 

2854 

95i  1 

6865 

4961 

3848 

3i 

3o 

58go45 

612801 

637070 

661886 

687281 

713293 

739961 

767327 

795436 

824336 

3o 

3i 

9437 

320I 

7479 

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7709 

3732 

74o4i 1 

7789 

591 1 

4825 

29 

32 

9829 

36oi 

7888 

2723 

8i38 

4171 

0862 

8252 

6386 

53i4 

28 

33 

590221 

4002 

8298 

3i4i 

8567 

46n 

l3l2 

87i4 

6862 

58o3 

27 

34 

06 1 3 

4402 

8707 

356o 

8995 

5o5o 

1763 

9177 

7337 

6292  26 

35 

1006 

48o3 

9117 

3979 

9425 

5490 

22l4 

9640 

.  7813 

678225 

36 

1398 

52o4 

95-7 

4398 

9854 

59J0 

2666 

770104 

8290 

7272  24 

3? 

1791 

56o5 

9937 

48i8 

690283 

6370 

3i  1 7 

0567 

8766 

7762:23 

38 

2184 

6006 

64o347 

5237 

0713 

6810 

3569 

io3i 

9242 

8252  22 

39 

2577 

64o8 

0757 

5657 

n43 

7250 

4020 

1495 

9719 

874321 

4o 

592970 

616809 

64i 167 

666077 

691572 

717691 

744472 

771959 

800196 

829234  20 

4i 

3363 

7211 

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6497 

2003 

8i32 

4925 

2423 

0674 

9725 

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42 

3757 

76i3 

1989 

6917 

2433 

8573 

5377 

2888 

1 1 5i 

83o2i6 

18 

43 

4i5o 

8oi5 

2399 

7337 

2863 

9014 

583o 

3353 

1629 

0707 

l7 

44 

4544 

84i7 

2810 

7758 

3294 

9455 

6282 

38i8 

2107 

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16 

45 

4937 

8819 

3222 

8179 

3725 

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6735 

4283 

3585 

1691 

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46 

533i 

9221 

3633 

8599   4i56 

720339 

7189 

4743 

3o63 

2i83  14 

47 

5725 

9624 

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9020 

4587 

0781 

7642 

5- 1 4 

3542 

2676J13 

48 

6120 

620026 

4456 

9442 

5oi8 

1223 

8096 

568o 

4o2I 

3i69|ia 

49 

65i4 

0429 

4863 

9863 

545o 

1 665 

8549 

6i46 

45oo 

366j  1 1 

5o| 596908 

620832  64528o 

670284 

695881 

722108 

749003 

776612 

804979 

834i55  10 

5i 

73o3 

12351   5692 

0706 

63i3 

255o 

9458 

7078 

5458 

4648 

9 

52 

7698 

i638|  6io4 

1128 

6745 

2993 

9912 

7545 

593S 

5i42 

8 

53 

8o93 

2042I  65i6 

i55o 

7177 

3436 

75o366 

8012 

64iS 

5636 

7 

54 

8488 

2445 

6929 

1972 

7610 

3879 

0821 

8479 

6S98 

6i3o  6 
6624  5 

55 

8883 

2849 

7342 

2394 

8042 

4323 

1276 

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7379 

56 

9378 

3253 

7755 

2817 

8475 

4766 

1731 

94i4 

7859 

7119 

4 

57 

5674 

3657 

8168 

324o 

8908 

52IO 

2187 

9881 

834o 

7614 

3 

58 

600069 

4o6i 

858i 

3662 

934 1 |   5654 

2642 

780349 

8821 

8109 

2 

59 

o465 

4465 

8994 

4o85 

977-4J   6098 

3o98 

0817 

93o3 

8604 

1 

| 

59° 

58°  ;  57° 

56°  |  55Q    |  54° 

53° 

52J  j  51° 

50° 

1 

Natural  Co-tangents. 

to] 

*/ 6.53  J  6.67 

6.8a 

6.97  1  7.14 
1 

7.3, 

7.5o  |  7.70  |  7.93 

s.i4 

124 


JNaiurax.    Sines. 


i 

r 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

I 

O 

642788 

656o59 

669131 

681998 

694658 

707107 

719340 

73i354 

743i45 

754710 

60" 

I 

3oio 

6279 

9347 

2211 

4868 

7312 

9542 

i552 

3339 

4900 

59 

2 

3233 

6498 

9563 

2424 

5o77 

75i8 

9744 

1750 

3534 

5091 

58 

3 

3456 

6717 

9779 

2636 

5286 

7724 

9946 

1949 

3728 

5282 

57 

4 

3679 

6937 

9995 

2849 

5495 

7929 

720148 

2147 

3923 

5472 

56 

5 

3901 

7i56 

67021 1 

3o6i 

5704 

8i34 

0349 

2345 

4117 

5663 

55 

6 

4124 

7375 

0427 

3274 

5913 

834o 

o55i 

2543 

43l2 

5853 

54 

7 

4346 

7^94 

0642 

3486 

6122 

8545 

0753 

2741 

45o6 

6o44 

53 

8 

4569 

7814 

o858 

3698 

633o 

8750 

0954 

2939 

4700 

6234 

52 

9 

4791 

8o33 

1074 

3911 

6539 

8956 

n56 

3i37 

4894 

6425 

5i 

IO 

645oi3 

658252 

671289 

6841,23 

696748 

709161 

721357 

733334 

745o88 

7566i5 

5o 

ii 

5236 

847i 

i5o5 

4335 

6957 

9366 

i559 

3532 

5282 

68o5 

49 

12 

5458 

8689. 

1721 

4547 

7i65 

957i 

1760 

3730 

5476 

699548 

i3 

568o 

8908 

1936 

4759 

7374 

9776 

1962 

3927 

5670 

7i85 

47 

i4 

5902 

9127 

2l5l 

4971 

7582 

9981 

2i63 

4l25 

5864 

7375 

46 

i5 

6124 

9346 

2367 

5i83 

7790 

710185 

2364 

4323 

6057 

7565 

45 

16 

6346 

9565 

2582 

5395 

7999 

0390 

2565 

4520 

625i 

7755 

44 

17 

6568 

9783 

2797 

5607 

8207 

0595 

2766 

4717 

6445 

7945 

43 

18 

6790 

660002 

3oi3 

58i8 

84i5 

0799 

2967 

49i5 

6638 

8i34 

4a 

J9 

7012 

0220 

3228 

6o3o 

8623 

1004 

3i68 

5lI2 

6832 

8324 

4i 

20 

647233 

660439 

673443 

686242 

698832 

71 1209 

723369 

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8818 

8712 

8354 

7740 

6868 

5734 

2 

59 

6963|   7832 

846o 

8846 

8985 

8875 

85i2 

7894 

7017 

588o 

1 

39°  |  38°   37° 

36° 

35° 

34° 

33° 

32°   31° 

30° 

.3 

a 

I 

Natural 

Co-sine 

s. 

tol"".3'°8 

3.02 

2.95 

2.88 

2.81 

2.75 

2.68 

2.60 

2.53 

a.46 

1 

Natural   Tangents. 


127 


i 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

o 

1.19175 

1.23490 

1.27994 

1.32704 

1.37638 

1.42815 

1.482  56" 

1.53986 

i.6oo33 

1.6C428 

60 

I 

9246 

3563 

8071 

a785 

7722 

2903 

8349 

4o85 

oi37 

6538 

59 

2 

9316 

3637 

8i48 

2865 

7807 

2992 

844a 

4i83 

0241 

6647 

58 

3 

9387 

3710 

8225 

2946 

7891 

3o8o 

8536 

4281 

o345 

6757 

57 

4 

9457 

3784 

83o2 

3026 

7976 

3169 

8629 

4379 

o449 

6867 

56 

5 

9528 

3858 

8379 

3107 

8060 

3258 

8722 

4478 

o553 

6978 

55 

C 

9599 

3931 

8456 

3187 

8i45 

3347 

8816 

4576 

0657 

7088 

54 

7 

9669 

4oo5 

8533 

3268 

8229 

3436 

8909 

4675 

0761 

7198 

53 

8 

9740 

4079 

8610 

3349 

83i4 

3525 

9003 

4774 

o865 

73o9 

52 

9 

981 1 

4i53 

8687 

343o 

8399 

36i4 

9097 

4873 

0970 

.  74i9 

5i 

IO 

1. 19882 

1.24227 

1.28764 

i.335ii 

1.38484 

1.43703 

1. 49 1 90 

1.54972 

1. 61074 

1.67530 

5o 

ii 

9953 

43oi 

8842 

3592 

8568 

3792 

9284 

5071 

1179 

7641 

49 

12 

1.20024 

4375 

8919 

3673 

8653 

388i 

9378 

5170 

1283 

7752 

48 

i3 

0095 

4449 

8997 

3754 

8738 

397o 

9472 

5269 

i388 

7863 

47 

i4 

0166 

4523 

9074 

3835 

8824 

4o6o 

9566 

5368 

1493 

7974 

46 

i5 

0237 

4597 

9152 

3916 

8909 

4i49 

9661 

5467 

1598 

8o85 

45 

16 

o3o8 

4672 

9229 

3998 

8994 

4239 

9755 

5567 

1703 

8196 

44 

»7 

0379 

4746 

93o7 

4079 

9079 

4329 

9849 

5666 

1808 

83o8 

43 

18 

o45 1 

4820 

9385 

4 1 60 

9165 

44i8 

9944 

5766 

1914 

8419 

42 

*9 

OJ22 

4895 

9463 

4242 

9250 

45o8 

i.5oo38 

5866 

2019 

853i 

4i 

20 

I.20593 

1.24969 

1. 29541 

1.34323 

1.39336 

1.44598 

i.5oi33 

1.55966 

1. 62125 

1.63643 

4o 

21 

o665 

5o44 

9618 

44o5 

9421 

4688 

0228 

6o65 

223o 

8754 

39 

22 

0736 

5n8 

9696 

4487 

9507 

4778 

o322 

6i65 

2336 

8866 

38 

23 

0808 

5193 

9775 

4568 

9593 

4868 

0417 

6265 

2442 

8979 

37 

24 

0879 

5268 

9853 

465o 

9679 

4958 

o5i2 

6366 

2548 

9091 

36 

25 

0951 

5343 

993i 

4732 

9764 

5o49 

0607 

6466 

2654 

9203 

35 

26 

1023 

54i7 

i. 30009 

48i4 

985o 

5i39 

0702 

6566 

2760 

9316 

34 

27 

1094 

5492 

0087 

4896 

9936 

5229 

0797 

6667 

2866 

9428 

33 

2» 

1166 

5567 

0166 

4978 

1.40022 

5320 

0893 

6767 

2972 

954i 

32 

29 

1238 

5642 

0244 

5o6o 

0109 

54io 

0988 

6868 

3079 

9653 

3i 

3o 

:  ai3io 

1. 25717 

i.3o323 

i.35i42 

1. 40195 

i.455oi 

i.5io84 

1.56969 

i.63i85 

1.69766 

3o 

3i 

i382 

5792 

o4oi 

5224 

028: 

5592 

1179 

7069 

3292 

9879 

29 

32 

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5867 

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5307 

0367 

5682 

1275 

7170 

3398 

9992 

28 

33 

,   i526 

5943 

o558 

5389 

o454 

5773 

1370 

7271 

35o5 

1. 70106 

27 

34 

1 598 

6018 

0637 

5472 

o54o 

5864 

i466 

7372 

36i2 

0219 

26 

35 

1670 

6093 

0716 

555.4 

0627 

5955 

i562 

7A7A 

37i9 

o332 

25 

36 

1742 

6169 

o795 

5637 

0714 

6o46 

i658 

7575 

3826 

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24 

3? 

1814 

6244 

0873 

5719 

0800 

6137 

1754 

7676 

3934 

o56o 

25 

38 

1886 

6319 

0952 

58o2 

0887 

6229 

i85o 

7778 

4o4i 

0673  22 

39 

i959 

6395 

io3i 

5885 

0974 

632o 

1946 

7879 

4i48 

078721 

4o 

J.2203I 

1. 26471 

i.3iiio 

1.35968 

1.41061 

i.464ii 

i.52o43 

1. 57981 

1.64256 

1. 70901  20 

4i 

2Io4 

6546 

1190 

6o5i 

u48 

65o3 

2139 

8o83 

4363 

ioi5  19 

42 

2I76 

6622 

1269 

6i34 

1235 

65g5 

2235 

8i84 

447i 

1129  18 

43 

2249 

6698 

1 348 

6217 

1322 

6686 

2332 

8286 

4579 

1244  17 

44 

2321 

6774 

1427 

63oo 

1409 

6778 

2429 

8388 

4687 

i358  16 

45 

2394 

6849 

1 507 

6383 

1497 

6870 

2525 

8490 

4795 

i473  i5 

46 

2467 

6925 

i586 

6466 

1 584 

6962 

2622 

8593 

4903 

i588  i4 

47 

2539 

7001 

1666 

654y 

1672 

7o53 

2719 

8695 

5ou 

1702  1  3 

48 

26l2 

7077 

1745 

6633 

i759 

7146 

2816 

8797 

5 1 20 

1817  .2 

49 

2685 

7i53 

1825 

6716 

1847 

7238 

2913 

8900 

5218 

i93-  ii 

5o 

:.22758 

1.27230 

1. 31904 

i.368oo 

1.41934 

i.4733o 

i.53oio 

1.59009 

i.65337 

i.7'j<>47  10 

5i 

283i 

73o6 

1984 

6883 

2022 

7422 

3107 

9io5 

5445 

216.',  0 

52 

2904 

7382 

2064 

6967 

21  IO 

75i4 

32o5 

9208 

5554 

227*  6 

53 

2977 

7458 

2144 

7o5o 

2198 

7607 

33o2 

93n 

5663 

2393 

7 

54 

3o5o 

7535 

2224 

7i34 

2286 

7699 

34oo 

94i4 

5772 

2509 

(i 

55 

3:23 

761 1 

23o4 

7218 

2374 

7792 

3497 

95i7 

588i 

2()2  5 

5 

56 

3196 

7688 

23S4 

7302 

2462 

7885 

3595 

9620 

5990 

2741  .; 

5? 

3270 

7764 

2464 

7386 

255o 

7977 

3693 

9723 

6099 

2857  3 

5  s 

3343 

7841 

2544 

7470 

2638 

8070 

3791 

9826 

6209 

2973  2  ; 

5i; 

34i6 

7917 

2624 

7554 

2726 

8i63 

?,sss 

993o 
32 

63iS 
31 

3o89  1  1 

39° 

38° 

37° 

3GJ 

:;.") ' 

3lJ 

33° 

30 

1 

c 
*-* 

Ni 

itural  C 

o-tanger 

its. 

P. 
to 

P. 

tz,  1.20 

1.25 

i.3i 

i.37 

1. 4.; 

i.5i 

i.59 

1.68 

1.78 

1.88 

128 


Natural    Sines. 


jj  60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

09° 

■ 
60 

o]  866025 

874620 

882948 

891007 

898794 

906308 

9i3545 

92o5o5 

9271841933580 

1 

6171 

4761 

3o84 

1 139 

8922 

643 1 

3664 

0618 

7293   3685 

59 

3 

63i6 

4902 

3221 

1270 

9049 

6554 

3782 

0732 

7402 

3789 

58 

3 

646 1 

5o42 

3357 

l402 

9176 

6676 

3900 

0846 

75io 

3893 

57 

4 

6607 

5i83 

3493 

i534 

9304 

6799 

4oi8 

0959 

7619 

3997 

56 

5 

6752 

5324 

3629 

1666 

943i 

6922 

4i36 

1072 

7728 

4ioi 

55 

6 

6897 

5465 

3766 

1798 

9558 

7044 

4254 

n85 

7836 

4204 

54 

7 

7042 

56o5 

3902 

1929 

9685 

7166 

4372 

1299 

7945 

43o8 

53 

8 

7187 

5746 

4o38 

2061 

9812 

7289 

4490 

l4l2 

8o53 

44i2 

52 

9 

733i 

5886 

4174 

2192 

9939 

74n 

4607 

i525 

8161 

45i5 

5i 

10 

867476 

876026 

884309 

892323 

900065 

907533 

914725 

921638 

928270 

934619 

5o 

11 

7621 

6167 

4445 

2455 

0192 

7655 

4842 

1750 

8378 

4723 

49 

12 

7765 

6307 

458 1 

2586 

0319 

7777 

4960 

i863 

8486 

4826 

48 

i3 

7910 

6447' 

4717 

2717 

o445 

7899 

5o77 

1976 

8594 

4929 

47 

i4 

8o54 

6587 

4§52 

2848 

0572 

8021 

5194 

2088 

8702 

5o32 

46 

i5 

8199 

6727 

4988 

2979 

0698 

8i43 

53u 

2201 

8810 

5i35 

45 

16 

8343 

6867 

5i23 

3no 

0825 

8265 

5429 

23i3 

8917 

5238 

44 

17 

8487 

7006 

5258 

324i 

0951 

8387 

5546 

2426 

9025 

534i 

43 

18 

8632 

7146 

5394 

337i 

1077 

85o8 

5663 

2538 

yi33 

5444 

42 

10 

8776 

7286 

5529 

35o2 

1203 

863o 

5779 

265o 

9240 

5547 

4i 

20 

8G8920 

877425 

885664 

893633 

901329 

908751 

915896 

922762 

929348 

(;3565o 

4o 

21 

9064 

7565 

5799 

3763 

1455 

8872 

6oi3 

2875 

9455 

5752 

39 

22 

9207 

7704 

5934 

3894 

i58i 

8994 

6i3o 

2986 

9562 

5855 

38 

23 

935i 

7844 

6069 

4024 

1707 

91 1 5 

6246 

3098 

9669 

5957 

37 

24 

9495 

'  7983 

6204 

4i54 

i833 

9236 

6363 

32io 

9776 

6060 

36 

25 

9639 

8122 

6338 

4284 

1958 

9357 

6479 

3322 

9884 

6162 

35 

26 

9782 

8261 

6473 

44i5 

2084 

9478 

65g5 

3434 

9990 

6264 

34 

27 

9926 

84oo 

6608 

4545 

2209 

9599 

6712 

3545 

930097 

6366 

33 

28 

870069 

8539 

6742 

4675 

2335 

9720 

6828 

3657 

0204 

6468 

32 

29 

0212 

8678 

6876 

48o5 

2460 

9841 

6944 

3768 

o3i  i 

6570 

3i 

3o 

S70356 

878817 

887011 

894934 

902585 

909961 

917060 

923880 

93o4i8 

936672 

3o 

3i 

0499 

8956 

7i45 

5o64 

2710 

910082 

7176 

399I 

o524 

6774 

29 

32 

0642 

9095 

7279 

5194 

2836 

0202 

7292 

4l02 

o63i 

6876 

28 

33 

0785 

92S3 

74i3 

5323 

2961 

o323 

7408 

42l3 

0737 

6977 

27 

34 

0928 

9372 

7548 

5453 

3o86 

o443 

7523 

4324 

oS43 

7079 

26 

35 

1071 

9510 

7681 

5582 

3210 

o563 

•  7639 

4435 

0950 

7181 

25 

3G 

1214 

9649 

78i5 

5712 

3335 

0684 

7755 

4546 

io56 

7282 

24 

37 

i357 

9787 

7949 

584i 

346o 

0804 

7870 

4657 

1162 

7383 

23 

38 

1499 

9925 

8o83 

5970 

3585 

0924 

7986 

4768 

1268 

7485  [22 

39 

1642 

88oo63 

8217 

6099 

3709 

io44 

8101 

4878 

i374 

758621 

4o 

871784 

880201 

88835o 

896229 

go3834 

91 1 164 

918216 

924989 

93i48o 

937687 

20 

4i 

1927 

0339 

8484 

6358 

3958 

1284 

833i 

5099 

i586 

7788 

l9 

42 

2069 

0477 

8617 

6486 

4o83 

i4o3 

8446 

52IO 

1 69 1 

7889 

l8 

43 

2212 

o6i5 

875i 

66i5 

4207 

i523 

856i 

5320 

1797 

799017 

44 

2354 

0753 

8884 

6744 

433i 

i643 

8676 

543o 

1902 

8091 

16 

45 

2496 

0891 

9017 

6873 

4455 

1762 

8791 

554i 

2008 

8191 

i5 

46 

2638 

1028 

9i5o 

7001 

4579 

1881 

8906 

565i 

2Il3 

8292 

i4" 

47 

2780 

1166 

9283 

7i3o 

47o3 

2001 

9021 

5761 

2219 

8393 

i3 

48 

2922 

i3o3 

9416 

7258 

4827 

2120 

9i35 

587i 

2324 

8493 

12 

49 

3o64 

i44i 

9549 

7387 

4g5i 

2239 

925o 

5980 

2429 

8593 

n 

5o 

873206 

881578:889682 

897515 

905075 

912358 

919364 

926090 

932534 

938694 

10 

5 1 

334? 

1716 

9815 

7643 

5i98 

2477 

9479 

6200 

2639 

8794 

9 

52 

3489 

i853 

9948 

7771 

5322 

2596 

9593 

63io 

2  744 

8894 

8 

53 

363i 

1990 

890080 

7900 

5445 

2715 

9707 

6419 

2849 

8994 

7 

54 

3772 

2127 

02 1 3 

8028 

5569 

2834 

9821 

6529 

2954 

9094 

6 

55 

3914 

2264 

o345 

8i56 

5692 

2953 

9936 

6638 

3o58 

9i94 

5 

56 

4o55 

2401 

0478 

8283 

58i5 

3072 

92oo5o 

6747 

3i63 

9294 

4 

57 

4196 

2538 

0610 

84n 

5939 

3190 

oi64 

6857 

3267 

9394 

3 

58 

4338 

2674 

0742   8539 

6062 

3309 

0277 

6966 

3372 

9493 

2 

59 

4479 

2811 

0874'   8666 

6i85 

3427 

0391 

7075 

3476 

9593 

1 

29° 

23°  !  27°  |  26° 

25° 

24° 

23° 

22° 

21° 

20° 

2 

Natural 

Co-sines 

tol».3-39 

2.3l 

2.24 

2. 16 

2.09 

2.01 

1  .q3 

1.86 

1.78 

1.70 

Natural    Tangents. 


129 


1 

GO0 

61° 

G2° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

o 

1.73205 

i.8o4o5 

1.88073 

1. 96261 

a.o5o3o 

a.i445i 

2.2460/ 

2.35585 

2.47509 

2.60509 

60 

I 

332i 

0529 

82o5 

6402 

5i82 

46i4 

4780 

5776 

7716 

0736 

59 

a 

3438 

o653 

8337 

6544 

5333 

4777 

4g56 

5967 

7924 

0963 

58 

3 

3555 

0777 

8469 

6685 

5485 

4940 

5i32 

6i58 

8i32 

1 190 

57 

4 

367i 

0901 

8602 

6827 

5637 

5io4 

5309 

6349 

8  34o 

i4i8 

56 

5 

3788 

1025 

8734 

6969 

579o 

5268 

M86 

654i 

8549 

1 646 

55 

6 

3905 

1  i5o 

8867 

71 1 1 

5942 

5432 

5663 

6733 

8758 

1874 

54 

7 

4022 

1274 

9000 

7253 

6094 

5596 

584o 

6925 

8967 

:-o3 

53 

8 

4i4o 

1 399 

9i33 

7395 

6247 

5760 

6018 

7118 

9177 

2332 

5a 

9 

4257 

1 524 

9266 

7538 

64oo 

5925 

'  6196 

73i  1 

9386 

256i 

5 1 

IO 

i.74375 

1. 81649 

1.89400 

1. 97681 

2.o6553 

2.16090 

2.26374 

2.37504 

2.49597 

2.62791 

5o 

ii 

4492 

1774 

9533 

7823 

6706 

6255 

6552 

7697 

9807 

3o2i 

49 

12 

46io 

1899 

9667 

7966 

6860 

6420 

6730 

7891 

2.5ooi8 

3252 

48 

i3 

4728 

2.02b 

9801 

8110 

7014 

6585 

6909 

8084 

0229 

3483 

47 

i4 

4846 

2i5o 

9935 

8253 

7167 

675i 

7088 

8279 

o44o 

37i4 

46 

i5 

4964 

2276 

1.90069 

8396 

7321 

6917 

7267 

8473 

o652 

3945 

45 

16 

5o82 

2402 

0203 

854o 

7476 

7083 

7447 

8668 

0864 

4177 

44 

«7 

5200 

2528 

0337 

8684 

7630 

7249 

7626 

8863 

1076 

44io 

43 

18 

5319 

2654 

0472 

8828 

7785 

7416 

7806 

9o58 

1289 

4642 

4a 

*9 

5437 

2780 

0607 

8972 

7939 

7582 

7987 

9253 

l5o2 

4875 

4r 

20 

1.75556 

1.82906 

1.9074 1 

1.991 16 

2.08094 

2.17749 

2.28167 

2.39449 

2.51715 

2.65109 

4o 

21 

5675 

3o33 

0876 

9261 

825o 

7916 

8348 

9645 

1929 

5342 

39 

22 

5794 

3i  5g 

1012 

9406 

84o5 

8084 

8528 

984i 

2142 

5576 

38 

23 

5913 

3286 

"47 

955o 

856o 

825i 

8710 

2.4oo38 

2357 

58u 

37 

24 

6o32 

34i3 

1282 

9695 

8716 

8419 

8891 

0235 

2571 

6o46 

36 

25 

6i5i 

354o 

i4i8 

9841 

8872 

8587 

9073 

o432 

2786 

6281 

35 

26 

6271 

3667 

i554 

9986 

9028 

8755 

9254 

0629 

3ooi 

65i6 

34 

27 

('•390 

3794 

1690 

2.00l3l 

9184 

8923 

9437 

0827 

3217 

6752 

33 

28 

65 10 

3922 

1826 

0277 

.  9341 

9092 

9619 

IO20 

3432 

6989 

3* 

29 

663o 

4049 

1962 

042  3 

9498 

9261 

9801 

1223 

3648 

7225 

3i 

3o 

1-76749 

1. 84177 

1.92098 

2.00569 

2.09654 

2.19430 

2.29984 

2.41421 

2.53865 

j  .67462 

3o 

3i 

6869 

43o5 

2235 

0715 

9811 

9599 

2.30167 

1620 

4082 

7700 

29 

3? 

6990 

4433 

237I 

0862 

9969 

9769 

o35i 

1819 

4299 

7937 

28 

33 

71 10 

456i 

25o8 

1008 

2.10126 

9938 

o534 

2019 

45i6 

8175 

27 

34 

723o 

4689 

2645 

n55 

0284 

2.20108 

0718 

2218 

4734 

84i4 

26 

35 

735i 

4818 

2782 

l302 

0442 

0278 

0902 

2418 

4952 

8653 

25 

36 

7471 

4946 

2920 

1449 

0600 

o449 

1086 

2618 

5170 

8892 

24 

37 

7592 

5075 

3o57 

1596 

0758 

0619 

1271 

2819 

5389 

9i3i 

23 

38 

77'3 

52o4 

3195 

1743 

0916 

0790 

i456 

3019 

56o8 

937i 

22 

39 

7834 

5333 

3332 

1891 

1075 

0961 

i64i 

3220 

5827 

9612 

21 

4o 

1.77955 

1.85462 

1.93470 

2.02039 

2.II233 

2.2II32 

2.31826 

2.43422 

2.56o46 

2.69853 

20 

4i 

8077 

5591 

36o8 

2187 

1392 

i3o4 

2012 

3623 

6266 

2.70094 

19 

42 

8198 

5720 

3746 

2335 

i552 

i475 

2197 

3825 

6487 

o335 

l8 

43 

83i9 

585o 

3885 

2483 

171 1 

1647 

2383 

4027 

6707 

o577 

17 

44 

844i 

5979 

4023 

263i 

1871 

1819 

2570 

423o 

6928 

0819 

l6 

45 

8563 

6109 

4162 

2780 

2o3o 

1992 

2756 

4433 

7i5o 

1062 

1.5 

46 

8685 

6239 

43oi 

2929 

2190 

2164 

2943 

4636 

737i 

i3o5 

i4 

47 

8807 

6369 

444o 

3078 

235o 

2337 

3i3o 

4839 

7593 

i548  i3 

48 

8929 

6499 

4579 

3227 

25l  1 

25lO 

33i7 

5o43 

78i5 

i79a!ia 

49 

905 1 

663o 

4718 

3376 

2671 

2683 

35o5 

5246 

8o38 

2o36  1 1 

5o 

1.79174 

1.86760 

1.94858 

2.o3526 

2.12832 

2.22857 

2.33693 

2.4545i 

2.58261 

2.72281 

10 

5i 

9296 

6891 

4997 

3675 

2993 

3o3o 

388 1 

5655 

8484 

2526 

9 

52 

9419 

7021 

5i37 

3825 

3i54 

32o4 

4»6y 

586o 

870& 

2771 

8 

53 

9542 

7i52 

5277 

3975 

33i6 

3378 

4258 

6o65 

8932 

3017 

7 

54 

9665 

7283 

54i7 

4 1 25 

3477 

3553 

4447 

6270 

9l5(r 

3263 

6 

55 

9788 

74 1 5 

5557 

4276 

36j9 

3727 

4636 

6476 

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3509 

5 

56 

99  ■ « 

7  546 

5698 

4426 

38oi 

3902 

48a5 

6(^2 

9606 

3756 

4 

5- 

i.Soo34 

7677 

5838 

4577 

3963 

4077 

5oi5 

6888 

9831 

4oo4 

3 

58 

01*58 

7809 

5979 

4728 

4 1 25 

4252 

52o5 

7o95 

2.60057 

42  5 1 

2 

59 

0281 

7941 

6120 

4879 

4428 

53  9  5 

7302 

0283 

4499 

1 

29°    | 

28°  | 

27° 

26° 

25 

21° 

23° 

22° 

21° 

20° 

i 

Na 

tural  C 

o-tangei 

ts. 

P. 

tol 

£2.00 

2.13 

2.27 

a.44 

2.62 

2.«a 

3.o5 

3.3i 

3.6i 

3.95 

130 


Natural    S  i  s  e  sl 


a 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

o 

939693 

945519I 951057 

9563o5 

961262 

965926 

970296 

974370 

978148 

981627 

60 

I 

9792 

56i3 

n46 

6390 

1342 

6001 

o366 

4435 

8208 

1 683 

59 

2 

9891 

5708 

1236 

6475 

1422 

6076 

o436 

45oi 

8268 

1738 

58 

3 

9991 

58o2 

i326 

656o 

i5o2 

6i5i 

o5o6 

4566 

8329 

i793 

57 

4 

940090 

5897 

i4i5 

6644 

i582 

6226 

o577 

463i 

8389 

1849 

56 

5 

0189 

599i 

i5o5   6729 

1662 

63oi 

0647 

4696 

8449 

1904 

55 

6 

0288 

6o85 

i5g4i   6814 

1741 

6376 

0716 

4761 

85o9 

i959 

54 

7 

0387 

6180 

1684;  6898 

1821 

645 1 

0786 

4826 

8569 

20l4 

53 

8 

o486 

6274 

i773 

6983 

1901 

6526 

o856 

4891 

8629 

2069 

52 

9 

o585 

6368 

1862 

7067 

1980 

6600 

0926 

4956 

8689 

2123 

5i 

IO 

940684 

946462 

951951 

957151 

962059 

956675 

970995 

975020 

978748 

982178 

5o 

ii 

0782 

6555 

2o4oi    7235 

2139 

6749 

io65 

5o85 

8808 

2233 

49 

12 

0881 

6649 

2129 

7319 

2218 

6823 

n34 

5149 

8867 

2287 

48 

i3 

0979 

6743 

22l8 

74o4 

2297 

6898 

I204 

52i4 

8927 

2342 

47 

i4 

1078 

6837 

23o7i   7487 

2376 

6972 

1273 

5278 

8986 

2396 

46 

i5 

1176 

6930 

2396;   7571 

2455 

7046 

1342 

5342 

9045 

245o 

45 

16 

1274 

7024 

2484|   7655 

2534 

7120 

i4n 

54o6 

9io5 

25o5 

H 

*I7 

1372 

7117 

2573   7739 

2613 

7194 

1480 

547i 

9164 

2559 

43 

18 

1471 

7210 

2661 

7822 

2692 

7268 

i54g 

5535 

9223 

26i3 

42 

r9 

1569 

73o4 

2750 

7906 

2770 

7342 

1618 

5598 

9282 

2667 

4i 

20 

o4i666 

947397 

952838 

957990 

962849 

967415 

971687 

975662 

979341 

982721 

4o 

21 

1764 

7490 

2926 

8o73 

2928 

7489 

i755 

5726 

9399 

2774 

39 

22 

1862 

7583 

3oi5 

8i56 

3oo6 

7562 

1824 

579o 

9458 

2828 

38 

23 

i960 

7676 

3io3 

8239 

3o84 

7636 

1893 

5853 

95i7 

2882 

37 

24 

2057 

7768 

3191 

8323 

3i63 

7709 

1961 

59i7 

9575 

2935 

36 

25 

2i55 

7861 

3279 

84o6 

324i 

7782 

2029 

598o 

9634 

2989 

35 

26 

2252 

7954 

3366 

8489 

33i9 

7356 

2098 

6o44 

9692 

3o42 

34 

27 

235o 

8o46 

3454 

8572 

3397 

7929 

2166 

6107 

9750 

3096 

33 

a8 

2447 

8i39 

3542 

8654 

3475 

8002 

2234 

6170 

9809 

3149 

32 

29 

2544 

823i 

3629 

8737 

3553 

8075 

2302 

6233 

9867 

3202 

3 1 

3o 

942641 

948324 

9537i7 

958820 

96363o  968148 

97237O 

976296 

979925 

983255 

3o 

3i 

2739 

84i6 

38o4 

8902 

37o8   8220 

2438 

6359 

9983 

33o8 

29 

32 

2836 

85o8 

3892   8985 

3786 

8293 

25o6 

6422 

980041 

336i 

28 

33 

2932 

8600 

3979 

9067 

3863 

8366 

2573 

6485 

0098 

34i4 

27 

34'   3029 

8692 

4o66 

9i5o 

3941 

8438 

2641 

6547 

oi56 

3466 

26 

35   3126 

8784 

4i53 

9232 

4oi8 

85n 

2708 

6610 

02l4 

3519 

25 

36 

3223 

8876 

4s4o 

93i4 

4095 

8583 

2776 

6672 

O27I 

357i 

24 

37 

3319 

8968 

4327 

9396 

4i73 

8656 

2843 

6735 

o329 

3624 

23 

38 

3416 

9059 

44i4 

9478 

425o 

8728 

2911 

6797 

o386 

3676 

22 

39 

35i2 

9i5i 

45oi 

9560 

4327 

8800 

2978 

6859 

o443 

3729 

21 

4o 

943609 

949243 

954588 

959642 

964404 

968872 

973o45 

976921 

98o5oo 

983781 

20 

4i 

3705 

9334 

4674 

9724 

448 1 

8944 

3lI2 

6984 

o558 

3833 

J9 

42 

38oi 

9425 

4761 

9805 

4557 

9016 

3i79 

7046 

06 1 5 

3885 

18 

43 

3897 

95l7 

4847 

9887 

4634 

9088 

3246 

7108 

0672 

3937 

17 

44 

3993 

9608 

4934 

9968 

471 1 

9l59 

33i3 

7169 

0728 

3989 

16 

45 

4089 

9699 

5o20 

96oo5o 

4787   9231 

3379 

7231 

0785 

4o4i 

i5 

46 

4i85 

9790 

5io6 

oi3i 

4864   9302 

3446 

7293 

0842 

4092. 

i4 

47 

4281 

9881 

5192 

0212 

4940   9374 

35i2 

7354 

0899 

4i44 

i3 

43 

4376 

9972 

5278 

0294 

5oi6,   9445 

3579 

7416 

0955 

4196 

12 

49 

4472 

95oo63 

5364 

0375 

5093   9517 

3645 

7477 

1012 

4247 

11 

5o 

94456S 

95oi54 

95545o 

96o456 

965169  969588 

973712 

977539 

981068 

984298 

10 

5 1 

4663 

0244 

5536 

o537 

5245   9669 

3778 

7600 

1 1 24 

435o 

9 

52 

4758 

o335 

5622 

0618 

532i 

973o 

3844 

7661 

1181 

44oi 

8 

53 

4854 

o425 

57o7 

0698 

5397 

9801 

3910 

7722 

1237 

4452 

7 

54 

4949 

o5i6 

5793 

0779 

5473   9872 

3976 

7783 

1293 

45o3 

6 

55 

5o44|  0606 

5879 

0860 

5548   9943 

4042 

7844 

1 349 

4554 

5 

56 

5 1 3g j   0696 

5964 

0940 

5624  970014 

4108 

79°5 

i4o5 

46o5 

4 

57 

5234   0786 

6049 

1021 

5700   0084 

4i73 

7966   i46o 

4656 

3 

58 

5329 

0877 

6i34 

IIOI 

5775   oi55 

4239 

8026   i5i6 

4707 

Si 

59 

542Z 

0967 

6220 

1181 

585o   0225 

43o5 

8087!   1572]   4757 

1 

19> 

18° 

17° 

16°  |  15°  |  14° 

13°  |  12°  |  11°  [    10° 

c  ) 

Natural  Co-sine 

3. 

2  1 

P  Y             ' 

toi"!  l6a|  I>54 

1.46 

i.38 

:.3o 

1 .21 

i.i3 

i.o5   0.97  '  0.88 

Natural    Tangents. 


131 


70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78°  1  79° 

o 

2.74748 

2.90421 

3.07768 

3.27085 

3.48741 

3.73205 

4.01078 

4-33i48 

4-7o463  5.i4455 

60 

i 

4997 

0696 

8o73 

7426 

9125 

364o 

i576 

3723 

1 137   5256 

59 

a 

5246 

0971 

8379 

7767 

9509 

4075 

2074 

43oo 

i8i3,   6o58 

58 

3 

5496 

1246 

8685 

8109 

9894 

45 1 2 

2574 

4879   2490;   6863 

57 

4 

5746 

i523 

8991 

8452 

3.502791  495o>'   3076 

5459!   31701   7671 

56 

5   5996 

1799 

9298 

8795 

0666 

5388,   3578 

6o4o 

385i 

_  848o 

55 

ft   6247 

2076 

9606 

9i39 

io53 

5828 

4o8i   6623 

4534 

9293 

54 

7   6498 

2354 

9914'  9483;  i44i 

6268 

4586 

7207 

5219 

5.20107 

53 

8,   6750 

2632 

3.io222;   9829 

1820 

6709 

5092 

7793 

5906 

0925 

52 

9 

7002 

2910 

o532 

3.30174 

2219 

7l52 

5599 

838i 

6595 

1744 

5i 

to 

2.77254 

2.93189 

3.10842 

3.3o52i 

3.52609 

3.77595 

4.06107 

4.38969 

4.77286 

5.22566 

5o 

11 

75o7 

3468 

n53 

0868 

3ooi 

8o4o 

6616 

9560 

7978 

3391 

49 

12 

7761 

3748 

1464 

1216 

3393 

8485 

7127 

4-4oi52 

8673 

4218 

48 

i3 

8014 

4028 

i775 

i565 

3785 

8931 

7639 

0745 

937o 

5o48 

47 

i4 

8269 

4309 

2087 

1914 

4179 

9378J   8i52 

1 34o 

4.80068 

588o 

46 

i5 

8523 

4591 

2400 

2264 

4573 

9827-   8666 

1936 

0769 

67i5 

45 

16 

8778 

4872 

2713 

2614 

4968 

3.80276 

9182 

2534 

1471 

7553 

44 

17 

9o33 

5i55 

3027 

2965 

5364 

0726 

9699 

3i34 

2175 

8393 

43 

18 

9289 

5437 

334i 

33i7 

5761 

1177 

4.10216 

3735 

2882 

9235 

42 

J9 

9545 

5721 

3656 

3670 

6159 

i63o|   0736 

4338 

3590 

5.3oo8o 

4i 

20 

2.79802 

2.96004 

3.13972 

3.34o23 

3.56557 

3.82083 

4.ii256'4.44942 

4.843oo 

5.30928 

4o 

21 

2.80059 

6288 

4288 

4377 

6957 

2537 

1778 

5548 

5oi3 

1778 

39 

22 

o3i6 

6573 

46o5 

4732 

7357 

2992 

23oi 

6i55 

57?7 

263i 

38 

23 

0574 

6858 

4922 

5087 

7758 

3449 

2825 

6764 

6444 

3487 

3? 

24 

o833 

7i44 

524o 

5443 

8160 

3906 

335o 

7374 

7162 

4345 

36 

25 

1091 

743o 

5558 

58oo 

8562 

4364 

3877 

7986 

7882 

5206 

35 

26 

i35o 

7717 

5877 

6i58 

8966 

4824 

44o5 

8600 

86o5 

6070 

34 

27 

1610 

8oo4 

6197,   65i6i   9370 

5284 

4934 

9215 

933o 

6936 

33 

25 

1870 

8292 

65i7 

68751   9775 

5745 

5465 

9832 

4.90056 

78o5 

32 

29 

2i3o 

858o 

6838 

7234'3.6oi8i 

6208 

5997 

4.5o45i 

0785 

8677 

3i 

3a 

2.82391 

2.98868 

3.17159 

3.37594'3.6o588 

3.86671 

4-i653o 

4.51071 

4-9i5i6 

5.39552 

3o 

3i 

2653 

9i58 

748i 

7955;   0996 

7i36 

7064 

1693 

2249 

5.40429 

29 

3i 

2914 

9447 

7804 

83I? 

i4o5 

7601 

7600 

23i6 

2984 

1 309 

28 

33 

3i76 

9738 

8127 

8679 
9042 

1814 

8068 

8137 

2941 

3721 

2192 

27 

34 

3439 

3.00028 

845 1 

2224 

8536 

8675 

3568 

446o 

3o77 

26 

35 

3702 

0319 

8775 

9406 

a636 

9004 

92i5 

4196 

520I 

3966 

25 

36 

3965 

061 1 

9100 

977i 

3o48 

9474   9756 

4826 

5945 

4857 

24 

37 

4229 

0903 

9426 

3.4oi36 

346i 

994514.20298 

5458 

6690 

.  575i 

23 

38 

4494 

1196 

9752 

o5o2 

3874 

3.9041 7I   0842 

6091 

7438 

6648 

22 

39 

4758 

i489 

3.20079 

0869 

4289 

0890 

i387 

6726 

8188 

7548 

21 

4o 

2.85o23 

3.01783 

3. 20406 

3.4i236 

3.647o5 

3.91364 

4.21933 

4.57363 

4.98940 

5.4845i 

20 

4i 

5289 

2077 

0734 

i6o4 

5l21 

i83g 

2481 

8001 

9695 

g356 

l9 

42 

5555 

2372 

io63 

1973 

5538 

23i6 

3o3o 

864 1 

5.oo45i 

5.50264 

l8 

43 

5822 

2667 

1392 

2343 

5957 

2793 

358o 

9283 

1210 

1 1 76 

17 

44 

6089 

2963 

1722 

2713 

6376 

3271 

4i32 

9927 

1971 

2090 

l6 

45 

6356 

32G0 

2o53 

3o84 

6796 

375i 

4685 

4.60572 

2734 

3007 

i5 

46 

6624 

3556 

2384 

3456 

72I7 

4232 

5239 

1219 

3499 

3927 

i4 

47 

6892 

3854 

27l5 

3829 

7638 

47i3 

5795 

1868 

4267 

485i 

i3 

4S 

7161 

4i52 

3o48 

4202 

8061 

5196 

6352 

25i8 

5o37 

5777 

12 

4y 

743o 

445o 

338i 

4576 

8485 

568o 

691 1 

3 1 7 1 

5809 

6706 

1 1 

5o 

2.87700 

3.04749 

3.237i4 

3.44951 

3.68909 

3.c;6i65 

4.27471 

4-63825 

5.o6584 

5.57638 

10 

5i 

7970 

5o49 

4049 

5327 

9335 

665i 

8o3a 

448o 

736o 

8  5  73 

9 

52 

8240 

5349 

4383 

5703 

9761 

7'39 

8595 

5i38 

8i3g   951 1 

8 

53 

85n 

5649 

4719   6080 

3.70188 

7627 

9 1 59 

5797 

8921  5.6o452 

7 

54 

8783 

5g5o 

5o55   6458 

0616 

8117 

9724 

6458 

9704   1397 

6 

55 

9o55 

6252 

5392 

6837 

1046 

86o74>3o29i 

7121  5.10490   n344 

5 

56 

9327 

6554 

5729 

7216 

1476   9099   0860'   7786   1279   3295 

4i 

57 

9600 

6857 

6067 

7596 

7977 

I9°7   9r>9-   i43o   8452   2069   4s48  3 

58 

9§73 

7160 

6406 

233S4.ooo86   2001   91 2 1   2862   5ao5  2 

5y  2.90147 

7464 

6745 

8359!   2771   o582 

2573   9791 
13°    \2>        11  ' 

6i65  1 

19° 

18° 

17°  i  16°  !  15°  i  14° 

~10° 

I 

Natural  Co-tangents. 

P-  P>  4  35 

4.82 

5.36 

f).<>i  j  6.79  !  7.73 

8. go  1  io.35   12.20 

'      1      1 

14.60 

132 


Natural    Sines3. 


.s 

80° 

81°  |  82° 

83° 

84° 

85° 

86° 

87° 

88° 

89°  | 

ol  q848o8 

987688 

990268 

992546 

994522 

996195  997564 

998630 

999391 

999848 

60 

,  I 

4858 

7734 

0309 

2582 

4552 

6220   7584 

8645 

9401 

9853'59 

2 

4909 

7779 

o349 

2617 

4583 

6245 

7604 

8660 

94" 

9358 

58 

3 

4959 

7824 

0389 

2652 

46i3 

6270 

7625 

8675 

9421 

9863  57 

4 

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985801 

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3272 

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57 

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58 

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6°    5° 

40 

3° 

2°    1° 

0°  I  . 

!  fi 

Natural  Co-sines. 

P.  P   fl 

tol".°-8u 

0.72 

o.63 

o.55 

o.46   o.38 

o.3o 

0.21 

o.i3 

o.o4 

Natural    Tangents. 


133 


d 

i 

80°  1  81° 

1 

82°  1  83° 

84° 

85° 

66° 

67° 

88° 

69° 

o 

5.67128J6.31375 
8094;   2566 

7.n537i8.i4435 

9.5i436 

ii.43oi 

14.3007 

1 9.08 1 1 

2*8.6363 

57.2900 

60 

I 

3o42 

6398 

4 1 06 

4685 

3607 

1879 

8771 

58.2612 

59 

2 

9064!   3761 

4553 

8370 

6791 

5072 

4212 

2959 

29.1220 

59.2659 

58 

3I5.70037I    4g6l 

6071 

8.2o352 

9490 

546i 

4823 

4o5i 

3711 

6o.3o58 

57 

4 

ioi3:   6 1 65 

7594 

2344 

9.62205 

5853 

5438 

5i56|   6245 

61.3829 

56 

5 

1992'   7374 

9125 

43451   4935 

6248 

6059 

6273   8823 

62.4992 

55 

6 

2974'   8587 

7.20661 

6355,   7680 

6645 

6685 

74o3;3o.i446 

63.6567  54 

7 

3960'   9804 

2204 

8376  9.70441 

70/.5 

7317 

8546 

4n6 

64.858o 

53 

8 

4949*6. 41026 

3754 

8.3o4o6 

3217 

7448 

7954,   9702 

6833 

66.io55 

52 

9 

5941 

2253 

53io   2446 

6009 

7853 

8596 

20.0872 

9599 

67.4019 

5i 

10 

5.76937 

6.43484 

7.26873 

8.34496 

9.78817 

11.8262 

14.9244 

20.2056 

3i.24i6 

68.75oi 

5o 

11 

7936 

4720 

8442 

6555 

9.81641 

8673 

9898 

3253 

5284 

70.i533 

49 

13 

8938 

5961 

7.30018 

8625 

4482 

9087 

i5.o557 

4465 

8205 

7i.6i5i 

43 

i3 

9944 

7206 

1600 

8.40705 

7338 

95o4 

1222 

5691 

32.1181 

73.1390 

47 

i4 

5  80953 

8456 

3190 

2795 

9.9021 1 

9923 

1893 

6932 

42i3 

74.7292 

46 

i5 

1966 

97101   4786 

4896 

3ioi 

12.0346 

2571 

8188 

73o3 

76.3900 

45 

16 

2982 

6.50970 

6389 

7007 

6007 

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3254 

9460 

33.o452 

78.1263 

44 

17 

4ooi 

2234 

7999 

9128 

8931 

1201 

3943 

21.0747 

3662 

79.9434 

43 

16   5o24 

35o3 

9616 

8.51259 

10.0187 

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4638 

2049 

6935 

81.8470 

42 

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6o5i 

4777 

7.41240 

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83.8435 

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20 

5.87080 

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7.42871 

8.55555 

10.0780 

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21.4704 

34.3678 

85.9398 

4o 

21 

8n4 

7339 

4509 

7718 

1080 

2946 

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7i5i 

88.i436 

39 

23 

9i5i 

8627 

6i54 

9893 

i38i 

3390 

7483 

7426 

35.0695 

90.4633 

38 

23 

5.90191 

9921 

7806 

8.62078 

i683 

3838 

8211 

88i3 

43i3 

92.9085 

37 

24 

.  1236 

6.61 2 19 

9465 

4275 

1988 

4288 

8945 

22.0217 

8006 

95.4895  36 

25 

2283 

2523 

7-5i  i32 

6482 

2294 

4742 

9687 

i64o 

36.1776 

98.2179:35 

26 

3335 

383i 

2806 

8701 

2602 

5i99 

i6.o435 

3o8i 

5627 

101.107  34 

2-7 

4390 

5 1 44 

448? 

8.70931 

2913 

566o 

1 190 

454i 

9560 

104.171I33 

28 

5448 

6463 

6176 

3i72 

3224 

6124 

1952 

6020 

37.3579 

107.42632 

29 

65io 

7787 

7872 

5425 

3538 

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2722 

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7686 

1 10.89213: 

3o 

5.97576 

6.691 16 

7.59575 

8.77689 

io.3854 

12.7062 

16.3499 

22.9038 

38.i885 

ii4.589|3o 

3i 

8646 

6.70450 

7.61287 

9964 

4172 

7536 

4283 

23.0577 

6177 

n8.54o  29  | 

^2 

9720 

1789 

3oo5 

8.82252 

4491 

8oi4 

5075 

2137 

39.0568  122.774(28  | 

33 

6.00797 

3i33 

4732 

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48i3 

8496 

5874 

37i8 

5o59 

127.32127 

34 

1878 

4483 

6466 

6862 

5i36 

8981 

6681 

532i 

9655 

132.219  26 

35 

2962 

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8208 

9i85 

5462 

9469 

7496 

6945 

4o.4358 

137.507  25 

36;   4o5i 

7199 

9957 

8.91520 

5789 

9962 

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8593 

9174 

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37 

5 1 43 

8564 

7.71715 

3867 

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24.0263 

4 1. 4 1 06 

149-465  23 

38 

6240 

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6227 

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9990 

1957 

9i58 

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39 

734o 

6.8i3i2 

5254 

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i46i 

17.0837 

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42.4335 

163.700  21 

4o 

6.o8444 

6.82694 

7.77035 

9.00983 

10.71 19 

13.1969 

17.1693 

24.54i8 

42.9641 

171.885  20 

4i 

9552 

4082 

8825 

3379 

7457 

2480 

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43.5o8i 

180.932J19 

42 

6.10664 

5475 

7.80622 

5789 

7797 

2996 

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44.o66i 

190.984 

18 

43 

1779 

6874 

2428 

8211 

8139 

35 1 5 

43i4  25.0798 

6386 

202.219 

17 

44 

2899 

8278 

4242 

9.10646 

8483 

4039 

52o5;  2644 

45.2261 

214-858  16 

45 

4023 

9688 

6064 

3og3 

8829 

4566 

6106 

45i7 

8294 

229.182  i5 

46 

5i5i 

6.91  io4 

7895 

5554 

9178 

5o98 

7015 

64i8 

46.4489 

245.552  14 

47 

628*3 

2525 

9734 

8028 

9529 

5634 

7934 

8348 

47.o853 

264.441  1 3 

48 

7419 

3952 

7.91582 

9.2o5i6 

9882 

6174 

8863|26.o3o7 

7395 

286.478  12 

49 

8559 

5385 

3438 

3oi6 

1 1.0237 

6719 

9802 

2296 

43.4i2i 

3i2.5ji!i  1 

5o 

6.197036.96823 

7.95302 

9-2553o 

11.0594 

13.7267 

18.0750 

26.43i6 

49.1039 

343.774  10 

5i 

6.2o85i 

8268 

7176 

8o58 

0954 

7821 

1 70S 

6367 

8i57 

381.971  9 

52 

2003 

9718 

9o58 

9.30599 

i3i6 

8378 

2677 

845o 

50.5485429.718!  8 

53 

3i6o 

7.01 1 74 

8.00948 

3i55 

16S1 

894o 

3655 

27.0566 

5i.3o32  491.106  7 

54 

4321 

2637 

2848 

5724 

2048 

95o7 

4645 

2715 

Vj.e--t>7  572.957J  6 

55 

5486 

4io5 

4756 

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2417 

14.0079 

5645 

4899 

8821687.549  5 

56 

6655 

5579 

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9.40904 

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6656 

7117  53.7086,859.436:  4 

5? 

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70  5  9 

8600 

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3i63 

1235 

7678 

9372  54.56i 3  1145.92!  3 

58 

9007 

8546 

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6i4i:   354<> 

1821 

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8781 

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9° 

b°    7°    6° 

4° 

1  3°    23    l3    03 

1 

Natural  C 

o-tange 

lis. 

P.  P.   0 

1 

22.19 

28.46 

37.83 

5.28 

7.88 

!  i3.oi 

1 

134 


Natural   Secants. 


Deg. 

0' 

10' 

20' 

30' 

40' 

50' 

P.  Pait 
to  1'. 

o 

I  I .OOOOOO 

1 .000004 

1 .000017 

1 .oooo38 

1 .000068 

1 .000106 

89 

2.5 

i 

OOOl52 

000207 

000271 

ooo343 

000423 

ooo5i2 

88 

7.6 

a 

■   000609 

000715 

ooo83o 

000953 

001084 

001224 

87 

I2.7 

3 

j   001372 

001529 

001695 

001869 

00205l 

002242 

86 

I7.8 

4 

002442 

oo265o 

002867 

003092 

oo3326 

003569 

85 

22.9 

5 

003820 

oo4o8o 

oo4348 

004625 

00491 1 

oo52o5 

84 

28.1 

6 

oo55o8 

oo5820 

006141 

006470 

006808 

007154 

83 

33.3 

7 

007510 

007874 

008247 

008629 

009020 

009419 

82 

38.6 

8 

009828 

010245 

010671 

011106 

on55o 

OI2003 

81 

43.9 

9 

OI2465 

012936 

oi34i6 

013905 

oi44o3 

014910 

80 

49.3 

IO 

: .015427 

1. 015952 

1 .016487 

1 .017030 

1. 017583 

I .018145 

79 

54.8 

ii 

018717 

019297 

019887 

020487 

021095 

021713 

78 

60.4 

12 

022341 

-  022977 

023624 

024280 

024945 

025620 

77 

66.0 

i3 

0263o4 

026998 

027702 

0284i5 

029138 

029871 

76 

71.8 

i4 

o3o6i4 

o3i366 

032128 

032900 

o33682 

034474 

75 

77-7 

i5 

035276 

o36o88 

036910 

037742 

o38584 

039437 

74 

83.7 

16 

040299 

041172 

o42o55 

042949 

o43853 

044767 

73 

89.8 

*7 

045692 

046627 

047573 

048029 

049496 

o5o474 

72 

96.1 

18 

o5i462 

o5246i 

o5347i 

054492 

o55524 

o56567 

7i 

102.6 

J9 

057621 

o58686 

059762 

060849 

061947 

o63o57 

70 

109.2 

20 

1. 064178 

1 .o653io 

•1  .o66454 

1 .067609 

1 .068776 

1 .069955 

69 

116. 1 

21 

071145 

072347 

073561 

074786 

076024 

077273 

68 

123.2 

22 

o78535 

079808 

081094 

082392 

083703 

o85o25 

67 

i3o.4 

23 

o8636o 

087708 

089068 

090441 

091827 

093225 

66 

i37.9 

24 

094636 

096060 

097498 

098948 

ioo4ii 

101888 

65 

145.6 

25 

103378 

104881 

106398 

107929 

109473 

mo3o 

64 

i53.7 

26 

1 12602 

114187 

1 15787 

1 1 7400 

1 19028 

120670 

63 

162.0 

27 

122326 

123997 

125682 

127382 

129096 

130826 

62 

170.7 

28 

132570 

134329 

i36io4 

137893 

139698 

i4i5i8 

61 

179.7 

29  . 

143354 

i452o5 

147073 

148956 

i5o854 

152769 

60 

189. 1 

3o 

1.154701 

1. 1 56648 

1 .i586i2 

1 .160592 

1. 162589 

1 . i646o3 

59 

198.9 

3i  1 

166633 

168681 

170746 

172828 

174927 

177044 

58 

209. 1 

32  | 

179178 

:8i33: 

i835oi 

i85689 

187895 

190120 

57 

219.7 

33 

192363 

194625 

196906 

199205 

20l523 

2o386i 

56 

230.9 

34 

206218 

208594 

210991 

2i34o6 

2l5842 

218298 

55 

242.6 

35  ! 

220775 

223271 

225789 

228327 

23o886 

233466 

54 

254.8 

36  i 

236o68 

238691 

24i336 

244oo3 

246691 

249402 

53 

267.7 

ll\ 

252i36 

254892 

257671 

260472 

263298 

266146 

52 

281.3 

38  I 

269018 

271914 

274834 

277779 

280748 

283741 

5i 

295.6 

39  • 

286760 

289803 

292872 

295967 

299088 

3o2234 

5o 

310.7 

4o  | 

1 ,3o54o7 

1.308607 

i.3ii833 

1 .3i5o87 

i.3i8368 

1 .321677 

49 

326.7 

^  1 

325oi3 

328378 

331771 

335192 

338643 

342123 

48 

343.6 

ft 

345633 

349172 

352742 

356342 

359972 

363634 

47 

36i.5 

43  | 

387327 

371052 

374809 

378598 

382420 

386275 

46 

38o.5 

44  1 

390164 

394086 

398042 

402032 

406057 

4ioii8 

45 

400.7 

45  ; 

414214 

4i8345 

4225l3 

426718 

430960 

435239 

44 

422'.  3 

46 

439557 

443912 

4483o6 

452740 

457213 

461726 

43 

445.3 

47 ! 

466279 

470874 

475509 

480187 

484907 

489670 

4a 

469.8 

48  j 

494477 

499327 

5o422I 

509160 

5i4i45 

519176 

4i 

496.2 

49  1 

524253 

529377 

534549 

539769 

545o38 

55o356 

4o 

524-4 

5o  | 

1 .555724 

1 .56n42 

1 .5666i2 

I .572134 

1 .577708 

1.583335 

39 

554.7 

c1  i 

589016 

594751 

6oo542 

6o6388 

612291 

6i825i 

38 

587.4 

52  ; 

624269 

63o346 

636483 

642680 

648938 

655258 

37 

622.7 

53  j 

661640 

668086 

674597 

681173 

6878i5 

694524 

36 

660.9 

54  1 

701302 

708148 

7i5oo4 

722051 

729110 

736241 

35 

702.2 

55  | 

743447 

750727 

758o84 

765517 

773029 

780620 

34 

747  •  2 

56  | 

788292 

796045 

8o388i 

811801 

819806 

827899 

33 

796.2 

57 ; 

836o78 

844348 

852707 

861159 

869704 

878344 

32 

849.8 

58  1 

887080 

895914 

904847 

9i388i 

923017 

932258 

3i 

908.5 

59 

94i6o4 

95io58 

960621 

970294 

980081  1 

9S9982 

3o 

97?.  0 

...  .  1 

60' 

50' 

40' 

30' 

20'  . 

10' 

Deg. 

■  " 

Natur 

a.1  Co-secai 

its. 

1 
J 

Natural   Secant b. 


135 


Deg. 

~6o~ 

0' 

10' 

20' 

30' 

40' 

,._  ., ,  .  _,  . — T 
50' 

P.  Part 
tol'. 

^. 000000 

a  o:oi36 

2,020393 

2.030772 

2.041276 

2.051906 

29 

io44 

6l 

062665 

073506 

084579 

095739 

107036 

n84?4 

28 

1123- 

62 

i3oo54 

141781 

i53655 

i6568i 

177859 

190195 

27 

I2IO 

63 

2026SC 

2i5346 

228168 

241 i58 

254320 

267657 

26 

i3o8 

64  !  281 1 72 

294869 

308750 

322820 

337083 

35i542 

25 

1417 

65 

366202 

38io65 

396137 

4n42i 

426922 

442645 

24 

i539 

66 

458593 

474773 

491187 

507843 

524744 

541896 

23 

1678 

67 

5593o5 

576975 

594914 

6i3i26 

63i6i8 

650396 

22 

i835 

68 

669467 

688387 

7o85i4 

7285o4 

748814 

769453 

21 

20l5 

69 

790428 

811747 

8334i9 

85545i 

877853 

900635 

20 

2222   1 

70 

2.923804 

2.947372 

2.971349 

2.995744 

3.020569 

3.o45835 

X9 

246l 

7i 

3.07i553 

3.097736 

3. 124396 

3.i5i545 

1 79 1 98 

207367 

18 

274o 

72 

236o68 

2653i5 

295123 

3255io 

356490 

388082 

17 

3o68 

73 

42o3o4 

453i73 

48671 1 

520937 

55587i 

59i536 

16 

3453 

74 

627955 

665i52 

7o3i5i 

741978 

781660 

822225 

i5 

3925 

75 

863703 

906125 

949522 

993929 

4.039380 

4.085913 

i4 

4492 

76 

4.133565 

4.182378 

4.232394 

4.283658 

3362i5 

3901 16 

i3 

5190 

77 

4454i 1 

502107 

56o4o8 

620226 

681675 

744821 

12 

6062 

78 

809734 

876491 

945169 

5.oi5852 

5.088628 

5. 163592 

11 

7171 

7? 

5-  24o843 

5.32o486 

5.4o2633 

487404 

574926 

665333 

10 

8612 

80 

5.758770 

5.855392 

5.955362 

6.o58858 

6. 166067 

6.277193 

9 

81 

6.392453 

6.5i2o8i 

6.636329 

6.765469 

6.899794 

7.039622 

8 

82 

7. 185297 

7.337191 

7.495711 

7.661298 

7.834433 

8.oi5645 

7 

83 

8.205509 

8.404659 

8.613790 

8.83367i 

9.o65i5i 

9.309170 

6 

84 

9.566772 

9.839123 

10. 12752 

io.43343 

10.75849 

1 1. io455 

5 

85 

n.4737i 

11.86837 

12.29125 

12.74549 

13.23472 

13.76311 

4 

86 

i4.33559 

14.95788 

i5. 63679 

i6.38o4i 

17. 19843 

18. 10262 

3 

!  8" 

19. 10732 

20.23028 

21.49368 

22.92559 

24.56212 

26.45o5i 

e 

86 

28.6537i 

3i.25758 

34.38232 

38.2oi55 

42.97571 

49.  n4o6 

1 

8c 

57.2J9869 

68.75736 

85.9456i 

1 i4.593o 

171.8883 

343.7752 

0 

60' 

50' 

40' 

30' 

20' 

10' 

D<*. 

Natural  Co-secants. 

LENGTHS  0 

F  CIRCULAR  ARCS. 

Degrees. 

Minutes.          Seconds. 

0 
I 

,oi74533 

0 
26 

.4537856 

0 
5i 

.8901 179 

/ 

I 

.0002909 

1  ; 

.0000048 

2 

.034906G 

27 

.4712389 

52 

.9075712 

2 

.ooo58iS 

2 

.0000097 

3 

.0523599 

28 

.4886922 

53 

.9250245 

3 

.0008727 

3 

.OOOOI45 

4 

.0698132 

29 

•5o6i455 

54 

.9424778 

4 

.ooii636 

4 

.0000194 

5 

.0872665 

3o 

.5235988 

55 

.959931 1 

5 

.ooi4544 

5 

.0000242 

6 

.1047198 

*,i 

.54io52i 

56 

•9773844 

6 

.0017453 

6 

.0000291 

7 

.  1221730 

32 

.5585o54 

5? 

.9948377 

7 

.0020362 

7 

.0000339 

8 

.1396263 

33 

.5759587 

58 

1 .0122910 

8 

.0023271 

8 

,oooo388 

9 

. 1J70796 

34 

.59341 19 

59 

1.0297443 

9 

.0026180 

9 

.oooo436 

10 

. 1745329 

35 

.6108652 

60 

1 .0471976 

10 

.0029089 

10 

.oooo485 

11 

. 1919862 

36 

.6283i85 

65 

1 . 1 34464o 

1 1 

.0031998 

1 1 

.oooo533 

12 

.2094396 

37 

.6457718 

70 

1 .2217305 

12 

.0034907 

12 

.oooo582 

;3 

.2268928 

38 

.663225i 

75 

1 .3089969 

i3 

.0037815 

i3 

.oooo63o 

x4 

.2443461 

39 

.6806784 

80 

1.3962634 

i4 

.0040724 

i4 

.0000679 

i5 

.2617994 

4o 

. 698 1 3 1 7 

85 

1.4835299 

i5 

.oo43633 

i5 

.0000727 

;6 

.2792527 

4i 

•7i5585o 

90 

1 .5707963 

16 

,oo46542 

16 

.0000776 

'7 

.2967060 

42 

•733o383 

100 

i.7453293 

17 

.oo4945i 

W 

.0000824 

:8 

,3i4i593 

43 

.7504916 

1 10 

1 .9198622 

18 

.oo52  36o 

18 

.0000873 

'9 

\33i6i26 

44 

.7679449 

120 

2.0943951 

*9 

,oo5526o 

»9 

.0000921 

20 

.3490659 

45 

.7853982 

i3o 

2.26S9280 

20 

.0058178 

20 

.0000970 

21 

.3665191 

46 

.8o285i5 

i4o 

2.44346io 

25 

.0072722 

25 

.0001212 

22 

.3839724 

47 

.8203047 

i5o 

2.6179939 

3o 

.0087266 

".> 

.oooi454 

23 

.4oi4257 

48 

.837758o 

160 

2.7925268 

4o 

.01 i6355 

4o 

.0001939 

24 

.4188790 

49 

.8*5521 1 3 

170 

2.9670597 

5o 

.oi45444 

5o 

. 0002424    ! 

\JL 

.4363323 

5o 

.8726646 

180 

3. 14^927 

.OI74533 

60  ' .0002909 

136 

Traverse  T. 

\  B  L  E 

. 

i 

■ 

Course. 

Dist.  1. 

Dist.  2. 

Dist.  3. 

Dist.  4. 

Dist.  5. 

Lat. 

Dcp. 

Lat 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

Dep. 

. 

o   / 

o  i5 

! 
I.OOOO 

0.0044 

2.0000 

0.0087 

3.0000 

O.Ol3l 

4-OOO0 

O.OI75 

5. oooo 

O.0218 

0    1    1 
89  45 

3o 

oooo 

0087 

I.9999 

OI75 

2.9999 

0262 

3.9998 

o349 

4.9998 

o436 

3o 

45 

0.9999 

oi3i 

9998 

0262 

9997 

o393 

9997 

o524 

9996 

o654 

:5 

I   o 

9998 

0175 

9997 

o349 

9995 

o524 

9994 

0698 

9902 

0873 

89   0 

i5 

9998 

0218 

9995 

o436 

9993 

o654 

9990 

0873 

99S8 

1091 

45 

3o 

9997 

0262 

9993 

o524 

9990 

0785 

9986 

1047 

9983 

1 309 

3o 

45 

9995 

o3o5 

9991 

06 1 1 

9986 

0916 

9981 

1222 

9977 

1527 

i5 

2   O 

9994 

o349 

9988 

0698 

9982 

1047 

9976 

I396 

9970 

1745 

88   0 

i5 

9992 

0393 

9985 

0785 

9977 

1 1 78 

!  9969 

l570 

9961 

1963 

45 

3o 

9990 

o436 

9981 

0872 

9971 

1 309 

9962 

1745 

.  9952 

2181 

3o 

45 

0.9988 

0.0480 

1.9977 

0.0960 

2.9965 

0.1439 

3.9954 

O.I9  I  9 

4.9942 

0.2399 

i5 

3   o 

9986 

o5a3 

9973 

1047 

9959 

1570 

9945 

2093 

993i 

2617 

87   0 

i5 

9984 

0567 

9968 

n34 

9952 

1701 

9936 

2268 

9920 

2835 

45 

3o 

9981 

0610 

9963 

1221 

9944 

i83i 

9925 

244^ 

9907 

3o52 

3o 

45 

9979 

o654 

9957 

i3o8 

9936 

1962 

9914 

26l6 

9893 

3270 

i5 

4  o 

9976 

0698 

995i 

1395 

9927 

2093 

9903 

2790 

9878 

3488 

86   0 

i5 

9973 

0741 

9945 

1482 

9918 

2223 

9890 

2964 

9863 

3705 

45 

3o 

9969 

o785 

9938 

1569 

9908 

2354 

9877 

3i38 

9846 

3923 

3o 

45 

9966 

0828 

993i 

i656 

9897 

2484 

9863 

33 1 2 

9828 

4i4o 

i5 

5   o 

9962 

0872 

9924 

1743 

9886 

26i5 

9848 

3486 

9810 

4358 

85   0 

i5 

0.9958 

0.0915 

1. 9916 

o.i83o 

2.9874 

0.2745 

3.9832 

o/366o 

4.9790 

0.4575 

45 

3o 

9954 

og58 

9908 

1917 

9862 

2875 

9816 

'3834 

9770 

4792 

3o 

45 

9950 

1002 

9899 

2004 

9849 

3oo6 

9799 

4oo8 

9748 

5009 

i5 

6   o 

9945 

io45 

9890 

2091 

9836 

3i36 

9781 

4i8i 

9726 

5226 

84   0 

i5 

994 1 

1089 

9S81 

2177 

9822 

3.266 

9762 

4355 

97°3 

5443 

45 

3o 

9936 

Il32 

9871 

2264 

9807 

3396 

9743 

4528 

9679 

566o 

3o 

45 

993i 

n75 

9861 

235i 

9792 

3526 

9723 

4701 

9653 

5877 

i5 

7   o 

9925 

1219 

985i 

2437 

9776 

3656 

9702 

4875 

9627 

6093 

83   0 

i5 

9920 

1262 

9840 

2524 

9760 

3786 

9680 

5o48 

9600 

63io 

45 

3o 

9914 

i3o5 

9829 

2611 

9743 

3916 

96^8 

5221 

9572 

6526 

3o 

45 

0.9909 

0.1349 

1. 9817 

0.2697 

2.9726 

0.4046 

3.9635 

0.5394 

4.9543 

0.6743 

i5 

6   o 

9903 

1392 

9805 

2783 

9708 

4175 

9611 

5567 

95i3 

6959 

82   0 

i5 

9897 

i435 

9793 

2870 

9690 

43o5 

9586 

5740 

9483 

7i75 

45 

3o 

9890 

1478 

9780 

2956 

9670 

4434 

9561 

5912 

945 1 

739° 

3o 

45 

9884 

l52I 

9767 

3o42 

965i 

4564 

1  9534 

6o85 

94 1 8 

7606 

i5 

9  ° 

9877 

i564 

9754 

3129 

9631 

4693 

9508 

6257 

9384 

7822 

81   0 

i5 

9870 

1607 

9740 

32 1 5 

9610 

4822 

9480 

643o 

935o 

8037 

45 

3o 

9863 

i65o 

9726 

33oi 

9589 

495.1 

945i 

6602 

93i4 

8252 

3o 

45 

9856 

i693 

9711 

3387 

9567 

5o8o 

9422 

6774 

9278 

8467 

i5 

IO   o 

9848 

1736 

9696 

3473 

9544 

5209 

9392 

6946 

9240 

8682 

80  0 

i5 

0.9840 

0.1779 

1. 9681 

o.3559 

2.9521 

0.5338 

3.9362 

0.7118 

4.9202 

0.8897 

45 

3o 

9833 

1822 

9665 

3645 

9498 

5467 

933o 

7289 

9163 

9112 

3o 

45 

9825 

i865 

9649 

3730 

9474 

5596 

9298 

7461 

9123 

9326 

i5 

II   o 

9816 

1908 

9633 

38i6 

9449 

5724 

9265 

7632 

9081 

9540 

79   ° 

i5 

9808 

1951 

9616 

3902 

9424 

5853 

9231 

7804 

9039 

9755 

45 

3o 

9799 

i994 

9598 

3987 

9398 

598i 

9197 

7975 

8996 

9968 

3o 

45 

9790 

2o36 

958i 

4073 

937* 

6109 

9162 

8i46 

8952 

1. 0182 

1 5 

12   O 

9781 

2079 

9563 

4i58 

9344 

6237 

9126 

83i6 

8907 

0396 

78   0 

i5 

9772 

2122 

9545 

4244 

93l7 

6365 

9089 

8487 

8862 

0609 

45 

3o 

1 

9763 

2164 

9526 

4329 

9289 

6493 

9052 

8658 

88i5 

0822 

3o 

45 

0.9753 

0.2207 

1.9507 

o.44i4 

2.9260 

0.6621 

3.9014 

0.8828 

4.8767 

i.io35 

i5 

i3   o 

9744 

225o 

9487 

4499 

9231 

6749 

8975 

8998 

8719 

1248 

77   0 

i5 

9734 

2292 

9468 

4584 

9201 

6876 

8935 

9168 

8669 

i46o 

45 

3o 

9734 

2334 

9447 

4669 

9171 

7003 

8895 

9338 

•8618 

1672 

3o 

45 

97i3 

2377 

9427 

4754 

9140 

7i3i 

8854 

95o7 

8567 

1884 

i5 

i4  o 

97o3 

2419 

9406 

4838 

9109 

7258 

8812 

9677 

85i5 

2096 

76   0 

i5 

9692 

2462 

9385 

4923 

9077 

7385 

8769 

9846 

8462 

23o8 

45 

3o 

9681 

25o4 

9363 

5oo8 

9044 

761 1 

8726 

i.ooi5 

8407 

2519 

3o 

45 

9670 

2546 

9341 

5092 

9011 

7638 

8682 

oi84 

8352 

2730 

i5 

i5   o 

9659 

2588 

93i9 

5i76 

8978  7765I 

8637 

o353 

8296 

2941 

75   0 

Coarse. 

.  .  .,  : 

Dep. 

Lat. 

Dep.  |  Lat. 

Dep.  |  Lat. 

Dep. 

Lat. 

Dep. 

Lat 

Dist.  1. 

1 

Dist.  2. 

1 

Dist.  3. 

Dist.  4. 

Dist.  5. 

Traverse  Table. 

137 

i  Coarse. 

Dist.  6. 

Dist.  7. 

Dist.  8. 

Dist.  <J. 

Dist.  10. 

i 

Lat 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

Lat  |  Dep. 

Lat  1  Dep. 

o   / 
o  i5 

5.9999 

O.0262 

6.9999 

o.o3o5 

7.9999 

0.0349 

8.9999  0.0393 

9.9999  o.o436 

0  1 
89  45 

3o 

9998 

o524 

9997 

06 1 1 

9997 

0698 

9997 

0785 

9996 

0873 

3o 

45 

9995 

0785 

9994 

0916 

9993 

1047 

9992 

1178 

999 « 

1 309 

i5 

1   o 

999 « 

1047 

9989 

1222 

9988 

1 396 

9986 

1571 

9985 

1745 

89   0 

i5 

998G 

1 309 

9983 

1527 

9981 

1745 

9979 

1963 

9976 

2181 

45 

3o 

9979 

1 571 

9976 

i832 

9973 

2094 

9969 

2356 

9966 

2618 

3o 

45 

9972 

i832 

9967 

2i38 

9963 

2443 

9958 

2748 

9953 

3o54 

i5 

2    O 

9963 

2094 

9957 

2443 

995i 

2792 

9945 

3i4i 

9939 

3490 

83   0 

i5 

9954 

2356 

9946 

2748 

9938 

3i4i 

993i 

3533 

9923 

3926 

45 

3o 

9943 

2617 

9933 

3o53 

9924 

3490 

9914 

3926 

9905 

4362 

3o 

45 

5.9931 

0.2879 

6.9919 

o.3358 

7.9908 

o.3838 

8.9896 

o.43i8 

9.9885 

0.4798 

i5 

3   o 

9918 

3i4o 

9904 

3664 

9890 

4i87 

9877 

4710 

9863 

5234 

87   0 

i5 

9904 

34o2 

9887 

3968 

9871 

4535 

9855 

5l02 

9839 

5669 

45 

3o 

9888 

3663 

9869 

4273 

985i 

4884 

9832 

5494 

9813 

6io5 

3o 

45 

9872 

3924 

985o 

4578 

9829 

5232 

9807 

5886 

9786 

654o 

i5 

4  o 

9854 

4i85 

9829 

4883 

9805 

558i 

9781 

6278 

9756 

6976 

86   0 

i5 

9835 

4447 

9808 

5i88 

9780 

5929 

9753 

6670 

9725 

74" 

45 

3o 

9815 

4708 

9784 

5492 

9753 

6277 

9723 

7061 

9692 

7846 

3o 

45 

9794 

4968 

9760 

5797 

9725 

6625 

9691 

7453 

9657 

8281 

i5 

5  o 

9772 

5229 

9734 

6101 

9696 

6972 

9658 

7844 

9619 

8716 

85   0 

i5 

5.9748 

0.5490 

6.9706 

o.64o5 

7.9664 

0.7320 

8.9622 

0.8235 

9.9580  0.9150 

45 

3o 

9724 

575i 

9678 

6709 

9632 

7668 

9586 

8626 

9540  9585 

3o 

45 

9698 

601 1 

9648 

7013 

9597 

8oi5 

9547 

9017 

9497  1.0019 

i5 

6  o 

9671 

6272 

9617 

73i7 

9562 

8362 

95o7 

9408 

9452 

o453 

84   0 

i5 

9643 

6532 

9584 

7621 

9525 

8709 

9465 

9798 

9406 

0887 

45 

3o 

9614 

6792 

955o 

7924 

9486 

9o56 

9421 

1.0188 

9357 

l320 

3o 

45!  9584 

7052 

95i5 

8228 

9445 

94o3 

9376 

0578 

93o7 

1754 

i5 

7  o,  9553 

73i2 

9478 

853i 

9404 

975o 

9329 

0968 

9255 

2187 

83   0 

i5'!  9520 

7572 

9440 

8834 

9360 

1.0096 

9280 

i358 

9200 

2620 

45 

3oj  9467 

7832 

9401 

9i37 

9316 

o442 

9230 

1747 

9144 

3o53 

3o 

45 

5.9452 

0.8091 

6.9361 

0.9440 

7.9269 

1.0788 

8.9178 

x.2137 

9.9087 

r.3485 

i5 

8  0 

9416 

835o 

93i9 

9742 

9221 

n34 

9124 

2526 

9027 

3917 

82   0 

i5 

9379 

8610 

9276 

i.oo44 

9172 

1479 

9069 

2914 

8965 

4349 

45 

3o 

9341 

8869 

9231 

0347 

9121 

1825 

901 1 

33o3 

8902 

4781 

3o 

45 

9302 

9127 

9i85 

0649 

9069 

2170 

8953 

3691 

8836 

5212 

i5 

9  ° 

9261 

9386 

9i38 

0950 

9015 

25i5 

8892 

4079 

8769 

5643 

Si   0 

i5 

9220 

9645 

9090 

1252 

8960 

2859 

883o 

4467 

8700 

6074 

45 

3o 

9177 

9903 

9040 

i553 

8go3 

32o4 

8766 

4854 

8629 

65o5 

3o 

45 

9i33 

1.0161 

8989 

i854 

8844 

3548 

8700 

524i 

8556 

6935 

i5 

10   0 

9088 

0419 

8937 

2i55 

8785 

3892 

8633 

5628 

848 1 

7365 

80   0 

1 5  5.9042 

1.0677 

6.8883 

1.2456 

7.8723 

1.4235 

8.8564 

i.6oi5 

g.84o4 

1.7794 

45 

3o 

8995 

0934 

8828 

2756 

8660 

4579 

8493 

64oi 

8325 

8224 

3o 

45 

8947 

1191 

8772 

3o57 

'  8596 

4922 

8421 

6787 

8245 

8652 

i5 

11   0 

8898 

i449 

87i4 

3357 

853o 

5265 

8346 

7173 

8i63 

9081 

79   ° 

i5 

8847 

1705 

8655 

3656 

8463 

5607 

8271 

7558 

8079 

9509 

45 

3o 

8795 

1962 

8595 

3956 

8394 

5949 

8193 

7943 

7992 

9937 

3o 

45 

8743 

2219 

8533 

4255 

8324 

6291 

8n4 

8328 

79o5 

2.o364 

i5 

12   0 

8689 

2475 

8470 

4554 

8252 

6633 

8o33 

8712 

78i5 

0791 

78   0 

i5 

8634 

2731 

84o6 

4852 

8178 

697/1 

795i 

9096 

7723 

1218 

45 

3o 

8578 

2986 

834i 

5i5i 

8io4 

73i5 

7867 

9480 

763o 

i644 

3o 

45|i5.852i 

1.3242 

6.8274 

1.5449 

7.8027 

1.76565J8.7781 

1.9863 

9.7534  2.2070 

i5 

i3   0 

8462 

3497 

8206 

5747 

795° 

7996 

7693 

2.0246 

7437 

2495 

77   0 

i5 

84o3 

3752 

8i37 

6o44 

7870 

8336 

7604 

0628 

7338 

2920 

45 

3o 

8342 

4007 

8066 

634i 

7790 

8676 

75i3 

IOIO 

7237 

3345 

3o 

45 

I  8281 

4261 

7994 

6638 

7707 

90 1 5 

7421 

1392 

7i34 

3769 

i5 

14  <S 

8218 

45i5 

793! 

6935 

7624 

9354 

7327 

1773 

7d3o 

4192 

76   0 

i5 

i  8i54 

4769 

7846 

7231 

7538 

9692 

723i 

2  I  54 

6923 

46i5 

45 

3o 

1  808c; 

5o23 

7770 

7527 

7452 

a.oo3o 

7i33 

2534 

j  68i5 

5o38 

5o 

45 

8023 

5276 

7693 

7822 

7364 

o368 

7034 

29 1 4 

6705 

546o 

i5 

1 5  0  795C 

5529 

76i5 

8117 

7274 

0706 

693: 

3294 

6593 

588a 

75   0 

Dep. 

Lnt 

|  itep. 

I. at 

Dep. 

Dep.  ',     Ub 

:  i>.p. 

|  Lat 

1  Connie. 

Dist.  6. 

Dist.  7. 

Di, 

t.  8. 

Dist.  0.    Disl 

-         J 

in. 

13S 


Traverse    Table. 


Ccraise. 

Dist.  1. 

Dist.  2. 

Dist.  3. 

Dist.  4. 

Dist  5. 

-  ■ '  ■  — — ■ 1 

Lat. 

Dep. 

Lat 

Dcp. 

Lat. 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

O     1 

i5  i5 

0.9648 

o.263o 

I.9296 

0.526l 

2.8944 

0.7891 

3.8591 

I.o52I 

4.8239 

i.3i52 

0    / 

74  45 

3o 

9636 

2672 

9273 

5345 

8909 

8017 

8545 

0690 

8182 

3362 

3o 

.  45 

9625 

2714 

9249 

5429 

8874 

8l43 

8498 

o858 

8l23 

3572 

i5 

16   o 

q6i2 

2756 

9225 

55i3 

8838 

8269 

845o 

1025 

8o63 

3782 

74   0 

i5 

9600 

2798 

9201 

5597 

8801 

8395 

8402 

1 193 

8002 

399i 

45 

3o 

9588 

284o 

9176 

568o 

8765 

852o 

8353 

i36i 

7941 

4201 

3o 

45 

9576 

2882 

9i5i 

5764 

8727 

8646 

83o3 

i528 

7879 

44io 

i5 

17  0 

9563 

2924 

9126 

584? 

8689 

8771 

8252 

1695 

7815 

4619 

73   0 

i5 

955o 

2965 

9100 

5931 

865i 

8896 

8201 

1862 

775i 

4827 

45 

3o 

9537 

3o07 

9074 

6o«4 

8612 

9021 

8149 

2028 

7686 

5o35 

3o 

45 

0.9524 

o.3o49 

1.9048 

0.6097 

2.8572 

0.9146 

3.8096 

1. 2195 

4.7620 

1.5243 

i5 

18   0 

95n 

3090 

9021 

6180 

8532 

9271 

8042 

236i 

7553 

545i 

72   0 

x5 

9497 

3i32 

8994 

6263 

8491 

9395 

7988 

2527 

7485 

5658 

45 

3o 

9483 

3i73 

8966 

6346 

845o 

95i9 

7933 

2692 

7416 

5865 

3o 

45 

9469 

32i4 

8939 

6429 

84o8 

9643 

7877 

2858 

7347 

6072 

i5 

19   0 

9455 

3256 

8910 

65n 

8366 

9767 

7821 

3o23 

7276 

6278 

71   0 

1 5 

9441 

3297 

8882 

6594 

8323 

9891 

7764 

3i88 

7204 

6485 

45 

30 

9426 

3338 

8853 

6676 

8279 

1.0014 

7706 

3352 

7132 

6690 

3o 

45 

9412 

3379 

8824 

6758 

)&235 

oi38 

7647 

35i7 

7059 

6896 

i5 

20   0 

9397 

3420 

8794 

6840 

8191 

0261 

7588 

368i 

6985 

7101 

70   0 

i5 

0.9382 

o.346i 

1.8764 

0.6922 

2.8146 

i.o384 

3.7528 

1.3845 

4.6910 

1.7306 

45 

3o 

9367 

35o2 

8733 

7004 

8100 

o5o6 

7467 

4oo8 

6834 

75io 

3o 

45 

935i 

3543 

8703 

7086 

8o54 

0629 

74o5 

4172 

6757 

77i5 

i5 

21   0 

9336 

3584 

8672 

7167 

8007 

0751 

7343 

4335 

6679 

7918 

69   0 

i5 

9320 

3624 

864o 

7249 

7960 

0873 

7280 

4498 

6600 

8122 

45 

3o 

93o4 

3665 

8608 

733o 

79i3 

0995 

7217 

466o 

652i 

8325 

3o 

45 

9288 

3706 

8576 

74n 

7864 

1117 

7152 

4822 

644o 

8528 

i5 

22   0 

9272 

3  746 

8544 

7492 

7816 

1238 

7087 

4984 

6359 

8730 

68   0 

i5 

9255 

3786 

85n 

7573 

7766 

i35g 

7022 

5i46 

6277 

8932 

45 

3o 

9239 

3827 

8478 

7654 

7716 

i48i 

6955 

5307 

6194 

9i34 

3o 

45 

0.9222 

0.3867 

1.8444 

0.7734 

2.7666 

1.1601 

3.6888 

1.5468 

4.6110 

1.9336 

i5 

23   0 

9205 

3907 

84io 

78i5 

7615 

1722 

6820 

5629 

6025 

9537 

67   0 

i5 

9188 

3947 

8376 

7895 

7564 

1842 

6752 

579o 

5940 

9737 

45 

3o 

9171 

3987 

834i 

7975 

7512 

1962 

6682 

5950 

5853 

9937 

3o 

45 

9i53 

4027 

83o6 

8o55 

7459 

2082 

6612 

6110 

5766 

2.0137 

i5 

24   0 

9i35 

4067 

8271 

8i35 

7406 

2202 

6542 

6269 

5677 

0337 

66      0 

i5 

9118 

4107 

8235 

8214 

7353 

2322 

6470 

642Q 

5588 

o536 

45 

3o 

9100 

4147 

8199 

8294 

7299 

244l 

6398 

6588 

5498 

0735 

3o 

45 

9081 

4187 

8i63 

8373 

7244 

256o 

6326 

6746 

5407 

0933 

i5 

25    O 

9063 

4226 

8126 

8452 

7189 

2679 

6252 

6905 

53i5 

ii3i 

65   0 

i5 

0.9045  0.4266 

1.8089 

o.853i 

2.7134 

1.2797 

3.6178 

1.7063 

4.5223 

2.1328 

45 

3o 

9026 

43o5 

8o52 

8610 

7078 

2915 

6io3 

7220 

5129 

i526 

3o 

45 

9007 

4344 

8oi4 

8689 

7021 

3o33 

6028 

7378 

5o35 

1722 

i5 

26   0 

8988 

4384 

7976 

8767 

6964 

3i5i 

5952 

7535 

494o 

1919 

64  .  0 

i5 

8969 

4423 

7937 

8846 

6906 

3269 

5875 

7692 

4844 

2Il4 

45 

3o 

8949 

4462 

7899 

8924 

6848 

3386 

5797 

7848 

4747 

23lO 

3o 

45 

893o 

45oi 

7860 

9002 

6789 

35o3 

57i9 

8oo4 

4649 

25o5 

i5 

27  0 

8910 

454o 

7820 

9080 

6730 

3620 

564o 

8160 

455o 

2700 

63   0 

i5 

8890 

4579 

7780 

9i57 

6671 

3736 

556i 

83i5 

445 1 

2894 

45 

3o 

8870 

4617 

7740 

9235 

6610 

3852 

548o 

8470 

435i 

3087 

3o 

45 

o.885o 

o.4656 

1.7700 

0.9312 

2.655o 

1.3968 

3.54oo 

1.8625 

4.4249 

2.3281 

i5 

28  0 

8829 

4695 

7669 

9389 

6488 

4084 

53i8 

8779 

4147 

3474 

62   0  1 

i5 

8809 

4733 

7618 

9466 

6427 

4200 

5236 

8933 

4o45 

3666 

45 

3o 

8788 

4772 

7576 

9543 

6365 

43i5 

5i53 

9086 

394i 

3858 

3o 

45 

8767 

48io 

7535 

9620 

63o2 

443o 

5069 

9240 

3836 

4049 

i5 

29   0 

8746 

4848 

7492 

9696 

6239 

4544 

4985 

9392 

373i 

4240 

6t   0 

i5 

8725 

4888 

745o 

9772 

6i75 

4659 

4900 

9545 

3625 

443 1 

45 

3o 

8704 

4924 

7407 

9848 

6111 

4773 

48i4 

9697I 

35i8 

4621 

3o 

45 

8682 

4962 

7364 

9924 

6o46 

4886 

4728 

9849 

34io 

48n 

i5 

3o  0 

8660 

5ooo 

7321 

r.0000 

5g8i 

5ooo 

464 1 

2.0000 

33oi 

5  000 

60   0 

Dcp. 

Lnt. 

Dep.  |  Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

Course. 

i! 

Dist.  1. 

i 

Dist.  2. 

Dist.  3. 

Dist.  4. 

Dist.  5. 

Traverse  Table. 

139 

Coarse 

Dist.  6. 

Dist.  7. 

Dist.  8. 

Dist.  9. 

Dist.  10. 

|    | 

Lat. 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

"0"  7~ 
74  45 

C    / 

i5  i5 

5.7887 

I.5782 

6.7535 

i.84i2 

7.7183 

2.Io42 

8.683i 

2.3673 

9.6479 

2.63o3 

3o 

7818 

6o34 

7454 

8707 

7090 

i379 

6737 

4o5i 

6363 

6724 

3o 

45 

7747 

6286 

7372 

9001 

6996 

I7l5 

6621 

443o 

6246 

7i44 

iG 

16   o 

7676 

6538 

7288 

9295 

6901 

2o5i 

65i4 

4807 

6126 

7564 

74   0 

i5 

7600 

6790 

72o3 

9588 

68o4 

2386 

64o4 

5i85 

6oo5 

7993 

45 

3o 

7529 

7041 

7H7 

9881 

6706 

2721 

6294 

556i 

5882 

8402 

3o 

45 

7454 

7292 

7o3o 

2.0174 

6606 

3o56 

6181 

5938 

5757 

8820 

i5 

t7   o 

7378 

7542 

6941 

o466 

65o4 

3390 

6067 

63i3 

563o 

9237 

73   0 

i5 

73oi 

7792 

685i 

0758 

6402 

3723 

5952 

6689 

55o2 

9654 

45 

3o 

7223 

8042 

6760 

1049 

6297 

4o56 

5835 

7064 

5372 

3.0071 

3d 

45 

5.7144 

1.8292 

6.6668 

2.l34l 

7.6192 

2.4389 

8.57i6 

2-7438 

9.5240 

3.0486 

i5 

18  o 

7o63 

854i 

6574 

i63i 

6o85 

4721 

5595 

7812 

5 1 06 

0902 

72   0 

i5 

6982 

8790 

6479 

1921 

5976 

5o53 

5473 

8i85 

4970 

i3i6 

45 

3o 

6899 

9038 

6383 

sail 

5866 

5384 

5349 

8557 

4832 

1730 

3o 

45 

6816 

9286 

6285 

25oi 

5754 

57i5 

5224 

8g3o 

4693 

2i44 

i5 

19   0 

673i 

9534 

6186 

2790 

564i 

6o45 

5o97 

9301 

4552 

2557 

71   0 

i5 

6645 

9781 

6086 

3078 

5527 

6370 

4968 

9672 

4409 

2969 

45 

3o 

6558 

2.0028 

5985 

3366 

54n 

6705 

4838 

3.oo43 

4264 

338i 

3o 

45 

I  64  7J 

6381 

0275 

5882 

3654 

5294 

7o33 

4706 

o4i3 

4n8 

3792 

i5 

20   0 

o52i 

5778 

3941 

5i75 

7362 

4572 

0782 

3969 

4202 

70   0 

i5 

5.6291 

2.0767 

6.5673 

2.4228 

7-5o55 

2.7689 

8.4437 

3.ii5i 

9.3819 

3.4612 

45 

3o 

6200 

IOI2 

5567 

45i5 

4934 

8017 

43oo 

1519 

3667 

5o2i 

So 

45 

6108 

1257 

5459 

4800 

48n 

8343 

4162 

1886 

35i4 

5429 

i5 

21   0 

6oi5 

i5o2 

535i 

5o86 

4686 

8669 

4022 

2253 

3358 

5837 

69   0 

i5 

5920 

1746 

524i 

537i 

456i 

8995 

388 1 

2619 

320I 

6244 

45 

3o 

5825 

I99O 

5129 

5655 

4433 

9320 

3738 

2985 

3o4« 

665o 

3o 

45 

5729 

2233 

5017 

5939 

43o5 

9645 

3593 

335o 

2881 

7o56 

i5 

22   0 

563i 

2476 

4903 

6222 

4i75 

9969 

3447 

3715 

2718 

746i 

68   0 

ID 

5532 

27x9 

4788 

65o5 

4o43 

3.0292 

3299 

4078 

2554 

7865 

45 

3o 

5433 

2961 

4672 

6788 

3910 

061 5 

3i49 

4442 

2388 

8268 

3o 

45 

5.5332 

2.32o3 

6.4554 

2.7070 

7.3776 

3.0937 

8.2998 

3.48o4 

9.2220 

3.&671 

i5 

23   O 

523o 

3444 

4435 

735i 

364o 

1258 

2845 

5i66 

2o5o 

9073 

67   0 

i5 

5127 

3o85 

43i5 

7632 

35o3 

i58o 

2691 

5527 

1879 

9474 

45 

3o 

5o24 

3925 

4194 

7912 

3365 

1900 

2535 

5887 

1706 

9875 

3o 

45 

4919 

4i65 

4072 

8192 

3225 

2220 

2378 

6247 

i53i 

4.0275 

i5 

24  0 

48i3 

44o4 

3948 

8472 

3o84 

2539 

2219 

6606 

i355 

0674 

66   0 

i5 

4706 

4643 

3823 

8750 

2941 

2808' 

2059 

6965 

1176 

1072 

45 

3o 

4598 

4882 

3697 

9029 

2797 

3i75 

1897 

7322 

0996 

14G9 

3o 

45 

4489 

5l20 

3570 

9306 

265i 

3493 

1733 

7679 

0814 

1866 

i5 

25   0 

4378 

5357 

3442 

9583 

25o5 

38o9 

i568 

8o36 

o63i 

2262 

65   0 

i5 

5.4267 

2.5594 

6.33i2 

2.9860 

7.2356 

3.4i25 

8.i4oi 

3.8391 

9.0446 

4.2657 

45 

3o 

4i55 

583i 

3i8i 

3.oi36 

2207 

444 1 

1233 

8746 

0259 

3o5i 

3o 

45 

4042 

6067 

3o49 

o4n 

2o56 

4756 

io63 

9100 

0070 

3445 

i5 

26  0 

3928 

63o2 

2916 

0686 

1904 

5070 

0891 

9453, 

8.9879 

3837 

64   0 

i5 

38i2 

6537 

2781 

0960 

1750 

5383 

0719 

9806 

9687 

4229 

45 

3o 

3696 

6772 

2645 

1234 

1595 

5696 

o544 

4-oi58 

9493 

4620 

3o 

45 

3579 

7006 

2509 

1507 

i438 

6008 

o368 

0509 

9298 

5oio 

i5 

27   0 

3460 

7239 

2370 

1779 

1281 

6319 

0191 

o859 

9101 

5399 

63   0 

i5 

3341 

7472 

223l 

2o5i 

1121 

663o 

0012 

1209 

8902 

57y7 

45 

3o 

3221 

77°5 

209I 

2322 

0961 

6940 

7.9831 

i557 

8701 

6i75 

3o 

45 

5.3099 

2.7937 

6.I949 

3.25g3 

7.0799 

3.7249 

7.9649 

4.1905 

8.8499 

4.656i 

i5 

28   0 

2977 

8168 

1806 

2863 

o636 

7558 

9465 

2252 

8295 

6947 

62   0 

i5 

2853 

8399 

1662 

3i32 

0471 

7866 

9280 

2599 

8089 

7332 

45 

3o 

2729 

863o 

i5 1 7 

34oi 

o3o5 

8173 

9094 

2944 

7S82 

7716 

3o 

45 

2604 

8859 

1371 

3669 

oi38 

8479 

8905 

3a89!   7673 

8099 

l5 

29  <b 

2477 

9089 

1223 

3937 

6.9970 

8785 

8716 

3633 

7462 

84^i 

61   0 

i5 

235o 

93'7 

1075 

42o3 

9800 

9090 

8525 

3976 

725o 

8862 

45 

3o 

2221 

9545 

0925 

4470 

9628 

9394 

8332 

43i8 

7o36 

9242 

3o 

45 

2092 

9773 

0774 

4735 

9456 

9697 

8i38 

4659 

6820 

_  9622 

i5 

3o  0 

1962 

3.ocoo 

0622 

5ooo 

9282 

4.0000 

7942 

5ooo 

66o3 

5.0000 

60   0 

Dep. 

Lat 

I).  p. 

Lat 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

Course,  j 

Dist.  6. 

Dist.  7. 

Dist.  8. 

Dist.  9. 

Dist.  10. 

.. 

140 


Traverse    Table. 


hoarse. 

Dist.  1. 

Dist.  2. 

Dist.  3. 

Dist.  4. 

Dist.  5. 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

Lat  j  Dep. 

o   / 

3o  i5 

0.8638 

o.5o38 

I.7277 

I.0075 

2.59l5 

i.5n3 

3.4553 

2.0l5l 

4.3192  2.5l8g 

0    / 
59  45 

3o 

8616 

5075 

7233 

Ol5l 

5849 

5226 

4465 

o3o2 

3o8i 

5377 

3o 

45 

]  8594 

5n3 

7188 

0226 

5782 

5339 

4376 

0452 

2970 

5565 

i5 

1i      o 

!  857s 

5i5o 

7l43 

o3oi 

57i5 

545 1 

4287 

0602 

2858 

5752 

59   0 

i5 

8549 

5i88 

7098 

0375 

5647 

5563 

4196 

075l 

2746 

5939 

45 

3o 

8526 

5225 

7o53 

o45o 

5579 

5675 

4io6 

O90O 

2632 

612S 

3o 

45 

85o4 

5262 

7007 

o524 

55n 

5786 

4oi4 

1049 

25i8 

63n 

i5 

Sa  o 

848o 

5299 

6961 

0598 

544i 

5898 

3922 

II97 

2402 

6496 

53   0 

i5 

8457 

5336 

6915 

0672 

5372 

6008 

3829 

1345 

2286 

6681 

45 

3o 

8434 

5373 

6868 

0746 

53o2 

6119 

3736 

1492 

2170 

6865 

3o 

45 

o.84io 

o.54io 

1. 6821 

1. 0819 

2.523l 

1.6229 

3.3642 

2.1639 

4-2052 

2.7049 

i5 

33   o 

8387 

5446 

6773 

0893 

5i6o 

6339 

3547 

I786 

I934 

7232 

57   0 

i5 

8363 

5483 

6726 

0966 

5o89 

6449 

345 1 

1932 

1814 

74i5 

45 

3o 

8339 

5519 

6678 

1039 

5017 

6558 

3355 

2077 

1694 

7597 

3o 

45 

83i5 

5556 

6629 

mi 

4944 

6667 

3259 

2223 

1573 

7779 

i5 

34  o 

8290 

5592 

658i 

1184 

487i 

6776 

3162 

2368 

1452 

7960 

56   0 

i5 

8266 

5628 

6532 

1256 

4798 

6884 

3o64 

25l2 

1329 

8i4o 

45 

3o 

8241 

5664 

6483 

i328 

4724 

6992 

2965 

2656 

1206 

8320 

3o 

i    45 

8216 

5700 

6433 

i4oo 

4649 

7100 

2866 

2800 

1082 

85oo 

i5 

35   o 

8192 

5736 

6383 

1472 

4575 

7207 

2766 

2943 

0958 

8679 

55   0 

i5 

0.8166 

0.5771 

1.6333 

1.1543 

2.4499 

i.73i4 

3.2666 

2.3o86 

4.0832 

2.8857 

45 

3o 

8141 

5807 

6282 

1614 

4423 

7421 

2565 

3228 

0706 

9o35 

3o 

45 

8116 

5842 

623i 

i685 

4347 

7527 

2463 

3370 

o579 

9212 

i5 

36   o 

8090 

5878 

6180 

i756 

4271 

7634 

236i 

35n 

o45 1 

9389 

54   0 

i5 

8064 

5913 

6129 

1826 

4193 

7739 

2258 

3652 

0322 

9565 

45 

3o 

8039 

5948 

6077 

1896 

4n6 

.7845 

2 1 54 

3793 

OI93 

974i 

3o 

45 

8oi3 

5983 

6o25 

1966 

4o38 

7950 

2o5o 

3933 

oo63 

9916 

i5 

37   0 

7986 

6018 

5973 

2o36 

3959 

8o54 

1945 

4073 

3.9932 

3.0091 

53   0 

i5 

7960 

6o53 

5920 

2106 

388o 

8i59 

1840 

4212 

9800 

0265 

45 

3o 

7934 

6088 

5867 

2175 

38oi 

8263 

1734 

435o 

9668 

o438 

3o 

45 

0.7907 

0.6122 

i.58i4 

1.2244 

2.3721 

1.8367 

3.1628 

2.4489 

3.9534 

3.o6i  1 

i5 

33  0 

7880 

6157 

5760 

23i3 

364o 

8470 

l520 

4626 

9401  0783 

52   0 

i5 

7853 

6191 

5706 

2382 

356o 

8573 

i4i3 

4764 

9266 

0955 

45 

3o 

7826 

6225 

5652 

245o 

3478 

8675 

i3o4 

4901 

9i3o 

1126 

3o 

45 

7799 

6259 

5598 

25i8 

3397 

8778 

1195 

5o37| 

8994 

1296 

i5 

39   0 

7771 

6293 

5543 

2586 

33i4 

8880 

1086 

5i73| 

8857 

i466 

5i   0 

i5 

7744 

6327 

5488 

2654 

3232 

8981 

0976 

53o8 

8720 

i635 

45 

3o 

7716 

636i 

5432 

2722 

3i49 

9082 

o865 

5443 

858i 

1804 

3o 

45 

7688 

63g4 

5377 

2789 

3o65 

9183 

0754 

557S 

8442 

1972 

i5 

4o  0 

7660 

6428 

532i 

2856 

2981 

9284 

0642 

5712 

83o2 

2139 

5o   0 

i5 

0.7632 

0.6461 

1.5265 

1.2922 

2.2897 

1.9384 

3.0529 

2.5845 

3.8162 

3.23o6 

45 

3o 

7604 

64g4 

5208 

2989 

2812 

9483 

o4i6 

5978 

8020 

2472 

3o 

45 

7576 

6528 

5i5i 

3o55 

2727 

9583 

o3o3 

6110 

7878 

2638 

i5 

4i  0 

7547 

656i 

5094 

3l2I 

2641 

9682 

0188 

6242 

7735 

28o3 

49  .0 

i5 

75i8 

6593 

5o37 

3i87 

2555 

9780 

0074 

6374 

7592 

2967 

45 

3o 

7490 

6626 

4979 

3252 

£469 

9879 

2.9958 

65o5 

7448 

3x3 1 

3o 

45 

7461 

6659 

4921 

33i8 

2382 

9976 

9842 

6635 

73o3 

3294 

i5 

42   0 

743i 

6691 

4863 

3383 

2294 

2.0074 

9726 

6765 

7i57 

3457 

48   0 

i5 

7402 

6724 

48o4 

3447 

2207 

0171 

9609 

6895 

701 1 

36i8 

45 

3o 

7373 

6756 

4746 

35i2 

2118 

0268 

9491 

7024 

6864 

3780 

3o 

45 

0.7343 

0.6788 

1.4686 

i.3576 

2.2030 

2.o364 

2.9373 

2.7152 

3.6716 

3.394o 

i5 

43   0 

73i4 

6820 

4627 

364o 

I94l 

o46o 

9254 

7280 

6568 

4ioo 

47   0 

i5 

7284 

6852 

4567 

3704 

i85i 

o555 

9i35 

7407 

6419 

4259 

45 

3o|  7254 

6884 

4507 

3767 

1761 

o65i 

9015 

7534 

6269 

44i8 

3o 

45 

7224 

6915 

4447 

383o 

1671 

0745 

8895 

7661 

6118 

4576 

i5 

44  0 

7193 

6947 

4387 

3893 

i58o 

o84o 

.8774 

7786 

5967 

4733 

46   0 

i5 

7i63 

6978 

4326 

3956 

i489 

0934 

8652 

7912 

58i5 

4890 

45 

3o 

7i33 

7009 

4265 

4oi8 

1398 

1027 

853o 

8o36 

5663 

5o45 

3o 

45 

7102 

7040 

4204 

4o8o 

i3o6 

1120 

8407 

8161 

5509 

5201 

i5 

45   0 

7071 

7071 

4142 

4i42 

I2l3 

I2l3 

8284 

8284 

5355 

5355 

45   0 

j 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Course. 

- 

1 

Dist.  1. 

Dist.  2. 

Dist.  3. 

Dist.  4. 

Dist.  5. 

Traverse  T 

ABLE 

141 

Course. 

Dist.  6. 

Dist.  7. 

Dist.  8. 

Dist.  9. 

Dist.  10. 

Lat  j  Dep. 

Lat 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

Let. 

Dep. 

O     / 

3o  1 5 

5.i83o 

3.0226 

6.0468 

3.5264 

6.9107 

4-o3o2 

7.7745 

4.534o 

8.6384 

5.0377 

0   / 
59  45 

3o 

1698 

o452 

o3nJ 

5528 

8930 

o6o3 

7547 

5678 

6i63 

0754 

3o 

45 

1 564 

0678 

oi58 

5791 

8753 

0903 

7347 

6016 

5941 

1 1 29 

i5 

3i   o 

i43o 

0902 

0002 

6o53 

8573 

I203 

7145 

6353 

57i7 

i5o4 

59  0 

i5 

1295 

1126 

5.9844 

63i4 

8393 

l502 

6942 

6690 

5491 

1877 

45 

3o 

n58 

i35o 

9685 

6575 

8211 

1800 

6738 

7025 

5264 

225o 

3o 

45 

1 02 1 

i573 

9525 

6835 

8028 

2097 

6532 

7359 

5o35 

2621 

i5 

3^   o 

o883 

i795 

9363 

7094 

7844 

2394 

6324 

7693 

48o5 

2992 

58   0 

i5 

0744 

2017 

9201 

7353 

7658 

2689 

6116 

8oa5 

4573 

336i 

45 

3o 

o6o3 

2238 

9o37 

761 1 

7471 

2984 

5905 

8357 

4339 

3730 

3o 

45 

5.o462 

3.2458 

5.8873 

3.7868 

6.7283 

4.3278 

7.5694 

4.8688 

8.4io4 

5.4097 

i5 

33   o 

0320 

2678 

8707 

8i25 

7094 

3571 

548o 

9018 

3867 

4464 

57   0 

i5 

0177 

2898 

854o 

838i 

6903 

3863 

5266 

9346 

3629 

4829 

45 

3o 

oo33 

3n6 

8372 

8636 

6711 

4i55 

5o5o 

9674 

3389 

5194 

3o 

45 

4.9888 

3334 

8203 

8890 

65i8 

4446 

4832 

5.oooi 

3i47 

5557 

i5 

34  o 

9742 

3552 

8o33 

9144 

6323 

4735 

46i3 

0327 

2904 

59i9 

56   0 

i5 

9595 

3768 

7861 

9396 

6127 

5o24 

4393 

o652 

2659 

6280 

.45 

3o 

9448 

3984 

7689 

9648 

5930 

53i2 

4171 

0977 

a4i3 

664 1 

3o 

45 

9299 

4200 

75i5 

9900 

5732 

56oo 

3948 

i3oo 

ai65 

7000 

i5 

35   o 

9149 

44i5 

734i 

4-oi5o 

5532 

5886 

3724 

1622 

191 5 

7358 

55   0 

i5 

4.8998 

3.4629 

5.7i65 

4-o4oo 

6.533i 

4.6172 

7.3498 

5.1943 

8.1664 

5.77i5 

45 

3o 

8847 

4842 

6988 

0649 

5129 

6456 

3270 

2263 

1412 

8070 

3o 

45 

8694 

5o55 

6810 

0897 

4926 

6740 

3o42 

2582 

1 157 

8425: 

i5 

36   o 

854i 

5267 

663i 

n45 

4721 

7023 

2812 

2901 

0902 

8779! 

54   0 

i5 

8387 

5479 

645 1 

1392 

45i6 

73o5 

258o 

3218 

0644 

9i3i 

45 

3o 

823i 

5689 

6270 

i638 

4309 

7586 

2347 

3534 

o386 

9482 

3o 

45 

8o75 

5899 

6088 

i883 

4ioo 

7866 

2Il3 

3849 

OI25 

9832! 

i5 

37  0 

7918 

6109 

5904 

2127 

3891 

8i45 

1877 

4i63 

7.9864 

6.0182 

53   0 

i5 

7760 

63i8 

5720 

237I 

368o 

8424 

1640 

4476 

9600 

0529 

45 

3o 

7601 

6526 

5535 

26i3 

3468 

8701 

l402 

4789 

9335 

0876 

3o 

45 

4.7441 

3.6733 

5.5348 

4-2855 

6.3255 

4.8977 

7.1162 

5.5ioo 

7.9069 

6.1222 

i5 

38   0 

7281 

6940 

5i6i 

3096 

3o4i 

9253 

0921 

54io 

8801 

i56G 

5a   0 

i5| 

7119 

7146 

4972 

3337 

2825 

9528 

0679 

57i8 

8532 

1909 

45 

3o 

6956 

735i 

4783 

3576 

2609 

9801 

0435 

6026 

8261 

225l 

3o 

45 

6793 

7555 

4592 

38i5 

2391 

5.0074 

0190 

6333 

7988 

2592 

15 

39   0 

6629 

7759 

44oo 

4o52 

2172 

o346 

6.9943 

6639 

77i5 

2932 

5i   0 

i5 

6464 

7962 

4207 

4289 

1951 

0616 

9695 

69431 

7439 

3271 

45 

3o 

6297 

8i65 

4oi4 

4525 

1730 

0886 

9446 

7247J 

7162 

36o8 

3o 

45 

6i3i 

8366 

3819 

4761 

1507 

n55 

9196 

755oi 

6884 

3944 

i5 

4o  0 

5963 

8567 

36a3 

4995 

1284 

i423 

8944 

785i 

6604 

4279 

5o  0 

i5! 

4.5794 

3.8767 

5.3426 

4.5229 

6.1059 

5.1690 

6.8691 

5.8i5i 

7.63-3 

6.4612 

45 

3o 

5624 

8967 

3228 

546i 

o832 

1956 

8437 

845o 

6o4i 

4945 

3o 

451 

5454 

9166 

3o3o 

5693 

o6o5 

2221 

8181 

87481 

5756 

5276 

i5 

4i  0 

5a83 

9364 

283o 

5924 

o377 

2485 

7924 

9o45i 

547i 

56o6 

49   0 

i5 

5no 

9561 

2629 

6i54 

_  0147 

2748 

7666 

9341! 

5 1 84 

5935 

45 

3o 

4g37 

9757 

2427 

6383 

5.9916 

3oio 

7406 

9636, 

4896 

6262 

3o 

45 

4763 

9953 

2224 

6612 

9685 

3271 

7i45 

9929 

46o6 

6588 

i5 

42  0 

4589 

4.oi48 

2020 

6839 

9452 

353o 

6883 

6.0222! 

43i4 

6913 

48   0 

i5 

44i3 

o342 

i8i5 

7066 

9217 

3789 

6620 

o5i3 

4022 

7237: 

45 

3o 

4237  o535! 

1609 

7291 

8982 

4<>4? 

6355 

0803, 

3728 

755y! 

3o 

45|4-4o59[4.0728j 

5.i4o3  4-75i6 

5.8746 

5.43o4 

6.6080 

6.10921 

7.3432 

6.7880 

l5 

43   olj  388i 

0920 

1 195 

7740 

85o8 

456o 

5822 

i38o' 

3i35 

8200 

47   ° 

1  ri      3702 

mi 

0986 

7963 

8270 

48i5 

5553 

1666 

2837 

85i8 

45 

3o  35a2 

i3oi 

0776 

8i85 

8o3o 

5o68 

5284 

I952 

2537 

8835 

3o 

45,  3342 
44  on  3 1 60 

1491 

o565 

84o6 

77^9 

532i 

5oi3 

2236 

2236 

9i5i 

i5 

1680 

o354 

8626 

7547 

5573 

474i 

2519 

1934 

9466 

46   0 

15 

2978 

1867 

oi4i 

8845 

73o4 

5823 

4467 

2801 

i63o 

9779i 

45 

3oi 

2795 

2o55 

4.9928 

9064 

7060 

6073 

4i93 

3o8a 

i3a5 

7.0091J 

3o 

45! 

2611 

224l 

97i3 

9281 

68i5 

6321 

3917 

336i! 

1019 

o4oi; 

i5 

45   0||  2426  2426! 

9497 

9497 

6569 

0569 

364o 

364o' 

071 1 

07II! 

45   0 

I 

Dep.  ]  Lot  | 

IVp. 

Lat  li  Dtp.  j  Lat 

Dep. 

Lat    Dep. 

Lat"J 

Covne. 

, 

Dist.  6. 

Dist 

.  7. 

Dist 

.  8. 

nist  9.       DistTio.  1 

142 

Meridional    Parts 

• 

LATITUDE. 

Min. 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

Min. 

o 

0.0 

60.0 

120.0 

180.1 

240.2 

3oo.z! 

360.7 

421. 1 

48i.6 

542.2 

6o3.i 

664.1 

725.3 

0 

I 

1.0 

61.0 

21.0 

81. 1 

4l-2 

01. i 

61.7 

22.1 

82.6 

43.3 

o4. 1 

65.3 

26.3 

I 

2 

2.0 

62.0 

22.0 

82.1 

42.2 

02.4 

62.7 

23.1 

83.6 

44.3 

o5.i 

66.1 

27.4 

2 

3 

3.0 

63.o 

23. 0 

83.i 

43.2 

o3.4 

63.7 

24.1 

84.6 

45.3 

06.1 

67.1 

28.4 

3 

4 

4.0 

64.o 

24.0 

84.1 

44.2 

o4.4 

64-7 

25.1 

85.6 

46.3 

07.1 

68.2 

29.4 

4 

5 

5.0 

65.o 

25. 0 

85.i 

45.2 

o5.4 

65.7 

26.1 

86.6 

47.3 

08.2 

69.2 

3o.5 

5 

6 

6.0 

66.0 

26.0 

86.1 

46.2 

06.4 

66.7 

27.1 

87.6 

48.3 

09.2 

70.2 

3i.5 

6 

7 

7.0 

67.0 

27.0 

87.1 

47.2 

07.4 

67.7 

28.1 

88.6 

49.3 

10.2 

71.2 

32.5 

7 

8 

8.0 

68.0 

28.0 

88.1 

48.2 

08.4 

68.7 

29.1 

89.6 

5o.3 

11. 2 

72.2 

33.5 

8 

9 

9.0 

69.0 

29.0 

89.1 

49-2 

09.4 

69.7 

3o.i 

90.7 

5i.4 

12.2 

73.3 

34.5 

9 

IO 

1 0.0 

70.0 

i3o.o 

190.1 

25o.2 

3io.4 

370.7 

43i.i 

491.7 

552.4 

6i3.2 

674.3 

735.6 

10 

ii 

II. 0 

71.0 

3i.o 

91. 1 

5l.2 

11.4 

71.7 

32.1 

92.7 

53.4 

14.2I  75.3 

36.6 

11 

12 

12.0 

72.0 

32.0 

92.1 

52.2 

12.4 

72.7 

33.i 

93.7 

54-4 

i5.3    76.3 

37.6 

12 

i3 

i3.o 

73.0 

33.o 

93.1 

53.2 

i3.4 

73.7 

34.2 

94.7 

55.4 

i6.3 

77.3 

38.6 

i3 

i4 

14.0 

74-o 

34.0 

94.1 

54.2 

14.4 

74.7 

35.2 

95.7 

56.4 

17.3 

78-4 

39.6 

14 

i5 

i5.o 

75.0 

35.o 

95.1 

55.2 

i5.4 

75.7 

36.2 

96.7 

57-4 

i8.3 

79-4 

40.7 

i5 

16 

16.0 

76.0 

36.o 

96.1 

56.2 

16.4 

76.8 

37.2 

97-7 

58.4 

19.3 

80.4 

4i-7 

16 

ll 

17.0 

77.0 

37.0 

97.1 

57.2 

17.5 

77.8 

38.2 

98.7 

59.4 

20.3 

81.4 

42.7 

17 

18 

18.0 

78.0 

38.o 

98.1 

58.2 

i3.5 

78.8 

39.2 

99.8 

6o.5 

21.3 

82.4 

43.7 

18 

r9 

19.0 

79.0 

39.0 

99.1 

59.2 

19.5 

79.8 

4o.2 

5oo.8 

6i.5 

22.4 

83.5 

44-8 

'9 

20 

20.0 

80.0 

i4o.o 

200.1 

260.2 

320.5 

38o.8 

44l.2 

5oi.8 

562.5 

623.4 

684.5 

745.8 

,2C 

21 

21.0 

81.0 

4i.o 

01. 1 

6i.3 

21.5 

81.8 

42.2 

02.8 

63.5 

244 

85.5 

46.8 

21 

22 

22.0 

82.0 

42.0 

02.1 

62.3 

22.5 

82.8 

43.2 

o3.8 

64.5 

25.4 

86.5 

47-8 

22 

23 

23.0 

83.o 

43.0 

o3.i 

63.3 

23.5 

83.8 

44-2 

04.8 

65.5 

26.4 

87.5 

48.9 

23 

24 

24.0 

84.0 

44.0 

o4-i 

64-3 

24.5 

84-8 

45.2 

o5.8 

66.6 

27.4 

88.6 

49.9 

24 

25 

25.0 

85.o 

45.0 

o5.i 

65.3 

25.5 

85.8 

46.3 

06.8 

67.6 

28.5 

89.6 

50.9 

25 

25 

26.0 

86.0 

46.o 

06.1 

66.3 

26.5 

86.8 

47-3 

07.8 

68.6 

29.5 

90.6 

51.9 

26 

27 

27.0 

87.0 

47.0 

07.1 

67.3 

27.5 

87.8 

48.3 

08.9 

69.6 

3o.5 

91.6 

53.o 

27 

28 

28.0 

88.0 

48.0 

08.1 

68.3 

28.5 

88.8 

49-3 

09.9 

70.6 

3i.5 

92.6 

54.o 

28 

29 

29.0 

89.0 

49.0 

09.1 

69.3 

29.5 

89.8 

5o.3 

10.9 

71.6 

32.5 

93.6 

55.o 

29 

3o 

3o.o 

90.0 

i5o.o 

210. 1 

270.3 

33o.5 

390.8 

45i.3 

511.9 

572.6 

633.5 

694.7 

756.0 

3o 

3i 

3i.o 

91.0 

5i.o 

11. 1 

71.3 

3i.5 

91.8 

52.3 

12.9 

73.7 

34.6 

95.7 

57.i 

3i 

32 

32.0 

92.0 

52.0 

12. 1 

72.3 

32.5 

92.9 

53.3 

13.9 

74.7 

35.6 

96.7 

58.i 

32 

33 

33.o 

93.0 

53.1 

i3.i 

73.3 

33.5 

93.9 

54.3 

14.9 

75.7 

36.6 

97-7 

59.1 

33 

34 

34.o 

94.0 

54.1 

i4.i 

74.3 

34.5 

94.9 

55.3 

15.9 

76.7 

37.6 

98.7 

60.1 

34 

35 

35,o 

95.0 

55.i 

i5.i 

75.3 

35.5 

95.9 

56.3 

16.9 

77-7 

38.6 

99.8 

61. 1 

35 

36 

36.o 

96.0 

56.i 

16.1 

76.3 

36.5 

96.9 

57.3 

18.0 

78.7 

39.6 

700.8 

62.2 

36 

37 

37.0 

97.0 

57.i 

17.1 

77.3 

37.5 

97-9 

58.4 

19.0 

79-7 

40.7 

01.8 

63.2 

37 

38 

38.o 

98.0 

58.i 

18.1 

78.3 

38.5 

98.9 

59.4 

20.0 

80.8 

41.7 

02.8 

64-2 

38 

39 

39.0 

99.0 

59.1 

19. 1 

79.3 

39.6 

99.9 

60.4 

21.0 

81.8 

42.7 

o3.8 

65.2 

39 

4o 

4o.o 

100. 0 

1 60. 1 

220.2 

280.3 

34o.6 

400.9 

46i.4 

522.0 

582.8 

643-7 

704.9 

766.3 

4o 

4i 

4i.o 

01. 0 

61. 1 

21.2 

8i.3 

4i.6 

01.9 

62.4 

23. 0 

83.8 

44-7 

05.9 

67.3 

4i 

42 

42.0 

02.0 

62.1 

22.2 

82.3 

42.6 

02.9 

63.4 

24-0 

84-8 

45.8 

06.9 

68.3 

42 

43 

43.o 

o3.o 

63.i 

23.2 

83.3 

43.6 

03.9 

64-4 

25.0 

85.8 

46.8 

07.9 

69.3 

43 

44 

44.0 

04.0 

64.1 

24.2 

84.3 

44.6 

04.9 

65.4 

26.0 

86.8 

47-8 

09.0 

70.4 

44 

45 

45.o 

o5.o 

65.i 

25.2 

85.3 

45.6 

05.9 

66.4 

27.1 

87.9 

48.8 

10.0 

71.4 

45 

46 

46.o 

06.0 

66.1 

26.2 

86.3 

46.6 

07.0 

67.4 

28.1 

88.9 

49-8 

I  1.0 

72.4 

46 

47 

47.0 

07.0 

67.1 

27.2 

87.3 

47-6 

08.0 

68.4 

29.1 

89.9 

5o.8 

12.0 

73.4 

47 

48 

48.o 

08.0 

68.1 

28.2 

88.3 

48.6 

09.0 

69.5 

3o.i 

90.9 

51.9 

i3.i 

74-5 

48 

49 

49.0 

09.0 

69.1 

29.2 

89.3 

49-6 

10. 0 

70.5 

3i.i 

91.9 

52.9 

14.1 

75.5 

49 

5o 

5o.o 

1 1 0.0 

170. 1 

23o.2 

290.3 

35o.6 

4n.o 

471-5 

532.1 

592.9 

653-9 

715.1 

776.5 

5o 

5i 

5i.o 

11. 0 

71. 1 

3l.2 

91.3 

5i.6 

12.0 

72.5 

33.1 

93.9 

54-9 

16.1 

77.5 

5i 

52 

52. 0 

12.0 

72.1 

32.2 

92.4 

52.6 

i3.o 

73.5 

34.i 

95.0 

55.9 

17.1 

78.6 

52 

53 

53.o 

i3.o 

73.i 

33.2 

934 

53.6 

i4-o 

74.5 

35.i 

96.0 

57.0 

18.2 

79.6 

53 

54 

54.o 

i4-o 

74.1 

34.2 

944 

54.6 

i5.o 

75.5 

36.2 

97.0 

58.o 

19.2 

80.6 

54 

55 

55.o 

i5.o 

75.i 

35.2 

95.4 

55.6 

16.0 

76.5 

37.2 

98.0 

59.0 

20.2 

81.7 

55 

56 

56.o 

16.0 

76.1 

36.2 

96.4 

56.6 

17.0 

77.5 

38.2 

99.0 

60.0 

21.2 

82.7 

56 

57 

57.0 

17.0 

77.1 

37.2 

97-4 

57.6 

18.0 

78.5 

39.2 

600.0 

61.0 

22.3 

83.7 

57 

58 

58.o 

18.0 

78.1 

38.2 

98.4 

58.6 

19.0 

79.5 

4o.2 

01. 0 

62.1 

23.3 

84-7 

58 

59 

59.0 

19.0 

79.1 

39.2 

99.4 

59.7 

20.0 

8o.5 

4l.2. 

02.1 

63.i 

24.3 

85.8 

59 

Meridional    Parts. 


143 


LATITUDE. 

9 

13° 

14° 

15° 

16° 

17°   I   18° 

19° 

20° 

21° 

22° 

23° 

24° 

1 

o 

786.8 

848.5 

910.5 

972.7 

io35.3 

1098.2 

n6i.5 

1225. 1 

1289.2 

i353.7 

i4i8.6 

i484-i 

0 

I 

87.8 

49-5 

ii.5 

73.8 

36.3 

99.3 

62.5 

26.2 

90.3 

54.8 

19.7 

85.2 

I 

2 

88.8 

5o.5 

12.6 

74.8 

37.4 

1  ioo.3 

63.6 

27.3 

91.3 

55.8 

20.8 

86.3 

a 

3 

89.9 

5i.6 

1 3.6 

75.9 

38.4 

01.4 

64-7 

28.3 

92.4 

56.9 

21-9 

87.3 

3 

4 

90.9 

52.6 

i4-6 

76.9 

39.5 

02.4 

65.7 

29.4 

93.5 

58.o 

23.o 

88.4 

4 

5 

91.9 

53.6 

1 5.7 

78.0 

4o.5 

o3.5 

66.8 

3o.4 

94.5 

59.0 

24-1 

89.5 

5 

6 

92.9 

54.7 

16.7 

79.0 

4i.6 

o4-5 

67.8 

3i.5 

95.6 

60.1 

25-1 

90.6 

b 

7 

94.0 

55.7 

17.7 

80.0 

42.6 

o5.6 

68.9 

32.6 

96.7 

61.2 

26-2 

91.7 

7 

8 

95.0 

56.7 

18.8 

81. 1 

43-7 

06.6 

70.0 

33.6 

97.8 

62.3 

27.3 

92.8 

6 

9 

96.0 

57.8 

19.8 

82.1 

44-7 

07.7 

71.0 

34-7 

98.8 

63.4 

28.4 

93.9 

9 

IO 

797.0 

858.8 

920.8 

983.2 

io45.8 

1 108.7 

1172.1 

1235.8 

1299.9 

i364.5 

1429.5 

1495.0 

10 

1 1 

98.1 

59.8 

21.9 

84.2 

46.8 

09.8 

73.1 

36.8 

i3oi.o 

65.6 

3o.6 

96.1 

1 1 

12 

99.1 

60.9 

22.9 

85.2 

47-9 

10.8 

74.2 

37.9 

02.0 

66.6 

3i.7 

97.2 

12 

i3 

800.1 

61.9 

23.9 

86.3 

48.9 

1 1.9 

75.2 

39.0 

o3.i 

67.7 

32.8 

98.3 

i3 

1 4 

01.2 

62.9 

25.0 

87.3 

49.9 

12.9 

76.3 

4o.o 

04.2 

68.8 

33.9 

99.4 

1 4 

i5 

02.2 

64.o 

26.0 

88.4 

5i.o 

i4-o 

77-4 

41.1 

o5.3 

69.9 

34-9 

i5oo.5 

i5 

16 

o3.2 

65.o 

27.0 

89.4 

52. 0 

1 5.o 

78.4 

42.2 

o6.3 

70.9 

36.o 

01.6 

16 

[7 

04.2 

66.0 

28.1 

90.4 

53.1 

16.1 

79.5 

43.2 

07.4 

72.0 

37.i 

02.7 

'7 

18 

o5.3 

67.1 

29.1 

91.5 

54-1 

17.1 

8o.5 

44-3 

o8.5 

73.i 

38.2 

o3.8 

18 

><; 

o6.3 

68.1 

3o.i 

92.5 

55.2 

18.2 

81.6 

45.4 

09.6 

74.2 

39.3 

o4-9 

UJ 

20 

807.3 

869.1 

931.2 

993.6 

io56.2 

1119.2 

1182.7 

1245.4 

i3io.6 

1375.3 

i44o.4 

i5o6.o 

20 

•:i 

08.4 

70.1 

32.2 

94.6 

57.3 

20.3 

83.7 

47-5 

11. 7 

76.4 

4i.5 

07.1 

21 

22 

09.4 

71.2 

33.3 

95.6 

58.3 

21.3 

84-8 

48.6 

12.8 

77-4 

42.6 

08.2 

22 

23 

10.4 

72.2 

34.3 

96.7 

59.4 

22.4 

85.8 

49.6 

1 3.8 

78.5 

43.7 

09.3 

23 

l:4 

11.4 

73.2 

35.3 

97-7 

60.4 

23.4 

86.9 

5o-7 

i4-9 

79.6 

44-8      10.4 

24 

25 

12.5 

74.3 

36.3 

98.8 

61.4 

24.5 

88.0 

5i.8 

16.0 

80.7 

45.8 

11. 5 

25 

26 

i3.5 

75.3 

37.4 

99-8 

62.5      35.5 

89.0 

52.8 

17.1 

81.8 

46.9 

12.6 

26 

-7 

i4.5 

76.3 

38.4 

1000.8 

63.5 

26.6 

90.1 

53.9 

18.1 

82.8 

48.o 

i3.7 

-7 

28 

i5.5 

77-4 

39.5 

01.9 

64-6 

27.6 

91. 1 

55.o 

19.2 

83.9 

49.1 

i4-8 

28 

29 

16.6 

78.4 

4o.5 

02.9 

65.6 

28.7 

92.2 

56.o 

20.3 

85.o 

5o.2 

1 5.9 

29 

3o 

817.6 

879.4 

941.6 

1004.0 

1066.7 

1129.7 

1193.2 

1257. 1 

1321.4 

i386.i 

i45i.3 

1517.0 

So 

3 1 

18.6 

8o.5 

42.6 

o5.o 

67.7 

3o.8 

94.3 

58.2 

22.5 

87.2 

52.4 

18.1 

3i 

3  2 

19.6 

8i.5 

43.6 

06.1 

68.8 

3i.8 

95.4 

59.2 

23.5 

88.3 

53.5 

19.2 

32 

33 

20.7 

82.5 

44-7 

07.1 

69.8 

32.9 

96.4 

6o.3 

24.6 

89.4 

54.6 

20.3 

33 

34 

21.7 

83.6 

45.7 

08.1 

70.9 

34.o 

97.5 

61.4 

25.7 

90.4 

55.6 

21.4 

34 

35 

22.7 

84-6 

46.7 

09.2 

72.0 

35.i 

98.5 

62.4 

26.7 

91.5 

56.7 

22.5 

35 

36 

23.8 

85.6 

47-8 

10.2 

73.0 

36.i 

99.6 

63.5 

27.B 

92.6 

57.8 

23.6 

36 

37 

24.8 

86.7 

48.8 

11. 3 

74.1 

37.2 

1200.7 

64-6 

28.9 

93.7 

58.9 

24.7 

37 

38 

25.8 

87.7 

49.9 

12.3 

75.i 

38.2 

01.7 

65.6 

3o.o 

94.8 

60.0 

25.8 

18 

39 

26.9 

88.7 

50.9 

i3.4 

76.2 

39.3 

02.8 

66.7 

3i.i 

95.8 

61. 1 

26.9 

59 

4o 

827.9 

889.8 

951.9 

ioi4-4 

1077.2 

1  i4o.3 

1203.9 

1267.8 

i332.i 

1396.9 

:462.2 

i528.o 

4o 

4i 

28.9 

90.8 

53.o 

1 5.4 

78.3 

4i.4 

04.9 

68.8 

33.2 

98.0 

63.3 

29.1 

4i 

42 

29.9 

91.8 

54.o 

16.5 

79.3 

42.4 

06.0 

69.9 

34.3 

99.1 

644 

3o.2 

42 

431   3i.o 

92.9 

55.i 

17.5 

80.4 

43.5 

07.1 

71.0 

35.3 

I400.2 

65.5 

3i.3 

43 

44|  32. c!  93.9 

56.i 

18.6 

81.4 

44-6 

08.1 

72.1 

36.4 

OI.3 

66.6 

32.4 

44 

45    33. 0    94-9 

57.i 

19.61    82.5 

45.6 

09.21     73.1 

37.5 

02.4 

67.7 

1     33.5 

45 

46    34-1 

96-0 

58.2 

20.6 

83.5 

46.7 

10.2      74.2 

38.6 

o3.4 

68.8 

34-6 

46 

47!  35.i 

97.0 

59.2 

21.7 

84-6 

47-7 

11. 3      75.3 

39.7 

o4.5 

69.8      35.7 

.:: 

48 

36.1 

98.0 

60.2 

22.7 

85.6 

48.8 

12.4      76.3 

40.7 

o5.6 

70.9      S6.8 

45 

49 

37.2 

99.1 

6i.3 

23.8 

867 

49.9 

i3.4 

77-4 

4i.8 

06.7 

72.0      379 

49 

5o 

838.2 

900.1 

962.3 

1024.8 

1087.7 

1 1 50.9 

1 2i4.5 

1278.5 

i34a-9 

1407.  s 

i473. 1  1539.0 

5c 

5i 

39.2 

on 

63.4 

25.9 

88.8 

52.0 

1 5.5 

79.5 

44.o 

08.8 

74.2      4o.i 

5< 

5  a 

4«.2 

02.2 

64-4 

26.9 

89.8 

53.0 

16.6 

80.6 

45.i 

09.9 

75.3     41.2 

5  2 

53 

4i.3 

o3.2 

65.5 

28.0 

909 

54-i 

17.7 

81.7 

46.1 

1 1.0 

76.4     42.3 

53 

54 

42.3 

04.3 

66.5 

29.0 

91.9 

55.i 

18.7 

82.8 

47-2 

1 2. 1 

77.5 

43.4 

54 

55 

43.3 

o5.3 

67.5 

3o.i 

93.0 

56.2 

19.8 

83.8 

48.3 

I  3.2 

78.6 

44-5 

55 

56 

44-4 

o6.3 

68.6 

3i.i 

94.0'     57.2 

20.9 

84-9 

49.4 

14.3 

79.7     45.6 

56 

5? 

45.4 

07.4 

!  69.6 

32.2 

95. il     58.3 

21.9 

86.0 

5o.4 

1 5.4 

80.8     46.7 

57 

58 

46-4 

08.4    70.7       33.2      96.1]      SyJi 

23.0 

S7.0 

5 1. 5 

16.5 

81.9      47-B 

58 

'■<; 

47-5 

09.4     7I.7        34.3        97.2        fm.4        24.1         SS-I 

52.6 

.7.5 

83.o      4&-9 

5_9 

14:4 

M  E  E  I  D  I  O  N  A  L 

Tart  a. 

LATITUDE. 

Mlc 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Miu. 

o 

i55o.o 

1616.5 

1683.5 

1751.2 

1819.4 

1888.4 

1958.0 

2028./J 

2099.5 

2171.5 

2244.3 

O 

I 

5i.i 

17.6 

84-6 

52.3 

20.6 

89.5 

59.2 

29.6 

2100.7 

72.7 

45.5 

I 

2 

52.2 

18.7 

85.8 

53.4 

21.7 

90.7 

60.4 

30.7 

01.9 

73.9 

46.8 

.  3 

53.3 

19.8 

86.9 

54.6 

22.9 

91.9 

61.6 

3i.9 

o3.i 

75.i 

48.o 

3 

4 

54-4 

20.9 

88.0 

55.7 

24.0 

93.0 

62.7 

33.i 

o4.3 

76.3 

49.2 

4 

5 

55.5 

22.0 

89.1 

56.8 

25.2 

94.1 

63.9 

34.3 

o5.5 

77.5 

5o.4 

5 

6 

56.6 

23.2 

90.3 

58.o 

26.3 

95.3 

65.o 

35.5 

06.7 

78.7 

5i.6 

6 

7 

57.7 

24.3 

91.4 

59.1 

27.5 

96.5 

66.2 

36.7 

07.9 

80.0 

52.9 

7 

8 

58.8 

25.4 

92.5 

60.2 

28.6 

97.6 

67-4 

37.8 

09.1 

81.2 

54.i 

8 

9 

59.9 

26.5 

93.6 

61.4 

29.7 

98.8 

68.5 

39.0 

io.3 

82.4 

55.3 

9 

10 

i56i.o 

1627.6 

1694.8 

1762.5 

l83o.9 

1899.9 

1969.7 

2040.2 

2111.5 

2183.6 

2256.5 

10 

ii 

62.1 

28.7 

95.9 

63.6 

32.0 

1901.1 

70.9 

41.4 

12.7 

84.8 

57.8 

1    ' 

12 

63.2 

29.8 

97.0 

64-8 

33.2 

02.3 

72.0 

42.6 

13.9 

86.0 

59.0 

12 

i3 

64-4 

3i.o 

98.1 

65.9 

34.3 

o3.4 

73.2 

43.8 

i5.i 

87.2 

60.2 

i3 

i4 

65.5 

32.1 

99.3 

67.0 

35.5 

04.6 

744 

44-9 

i6.3 

88.4 

61.4 

14 

i5 

66.6 

33.2 

1700.4 

68.2 

36.6 

05.7 

75.6 

46.i 

17.5 

89.6 

62.7 

i5 

16 

67.7 

34.3 

oi.5 

69.3 

37.8 

06.9 

76.8 

47.3 

18.7 

90.8 

63.9 

16  . 

17 

68.8 

35.4 

02.6 

70.5 

38.9 

08.1 

77-9 

48.5 

19.8 

92.0 

65.i 

17 

18 

69.9 

36.5 

o3.8 

71.6 

4o.i 

09.2 

79.1 

49-7 

21.0 

93.3 

66.3 

18 

l9 

71.0 

37.6 

o4-9 

72.7 

4l.2 

10.4 

80.2 

5o.8 

22.2 

944 

67.5 

l9 

20 

1572. 1 

i638.8 

1706.0 

1773.9 

1842.4 

191 1.5 

1981.4 

2052.0 

2123.^ 

2195.7 

2268.8 

20 

21 

73.2 

39.9 

07.1 

75.0 

43.5 

12.7 

82.6 

53.2 

24.6 

96.9 

70.0 

21 

22 

74-3 

4i.o 

o8.3 

76.1 

44.6 

i3.8 

83.7 

54.4 

25.8 

98.1 

71.2 

22 

23 

754 

42.1 

09.4 

77.2 

45.8 

i5.o 

84-9 

55.6 

27.0 

99.3 

72.5 

23 

24 

76.5 

43.2 

10. 5 

78.4 

46.9 

16.2 

86.1 

56.8 

28.2 

2200.5 

73.7 

24 

25 

77.6 

44.3 

11.6 

79.5 

48.1 

17.3 

87.3 

58.o 

29.4 

01.7 

74.9 

25 

26 

78.7 

45.5 

12.8 

8o.6 

49.2 

i8.5 

88.4 

59.1 

3o.6 

o3.o 

76.1 

26 

27 

79-8 

46.6 

13.9 

81.8 

5o.4 

19.6 

89.6 

6o.3 

3i.8 

o4-2 

77-4 

27 

28 

80.9 

47-7 

i5.o 

83.o 

5i.5 

20.8 

90.8 

6i.5 

33.o 

o5.4 

78.6 

28 

29 

82.1 

48.8 

16.1 

84-1 

52.7 

21.9 

92.0 

62.7 

34.2 

06.6 

79,8 

29 

3o 

i583.2 

1649.9 

1717.3 

1785.2 

i853.8 

1923. 1 

1993. 1 

2063.9 

2i35.4 

2207.8 

2281.0 

3o 

3i 

84-3 

5i.o 

18.4 

86.4 

55.o 

24.3 

94.3 

65.i 

36.6 

09.0 

82.3 

3i 

32 

854 

52.2 

19.5 

87.5 

56.i 

25.4 

95.5 

66.2 

37.8 

10.2 

83.5 

32 

33 

86.5 

53.3 

20.7 

88.6 

57.2 

26.6 

96.6 

67.4 

39.0 

11.4 

84-7 

33 

34 

87.6 

544 

21.8 

89.8 

58.4 

27.8 

97.8 

68.6 

4o.2 

12.7 

86.0 

34 

35 

88.7 

55.5 

22.9 

90.9 

59.6 

28.9 

99.0 

69.8 

4l-4 

13.9 

87.2 

35 

36 

89.8 

56.6 

24.0 

92.1 

60.7 

3o.i 

2000.2 

71.0 

42.6 

i5.i 

88.4 

36  i 

37 

90.9 

57.8 

25.2 

93.2 

61.9 

3i.3 

01.3 

72.2 

43.8 

i6.3 

89.7 

37 

38 

92.0 

58.9 

26.3 

94.3 

63.o 

32.4 

02.5 

734 

45.0 

17.5 

90.9 

38 

39 

93.i 

60.0 

27.4 

95.5 

64-2 

33.6 

03.7 

74-5 

46.2 

18.7 

92.1 

39 

4o 

i594.3 

1661.1 

I728.6 

1796.6 

i865.3 

1934.7 

2004.9 

2075.7 

2147.4 

2219.9 

2293.3 

4o 

4i 

95.4 

62.2 

29.7 

97.8 

66.5 

35.9 

06.0 

76.9 

48.6 

21.2 

94.6 

4i 

42 

96.5 

63.4 

3o.8 

98.9 

67.6 

37.i 

07.2 

78.1 

49.8 

22.4 

95.8 

42 

43 

97.6 

64-5 

31.9 

1800.0 

68.8 

38.2 

08.4 

79.3 

5i.o 

23.6 

97.0 

43 

44 

98.7 

65.6 

33.i 

01.2 

69.9 

39.4 

09.6 

8o.5 

52.2 

24.8 

98.3 

44 

45 

99.8 

66.7 

34.2 

02.3 

71. 1 

4o.5 

10.7 

81.7 

53.4 

26.0 

99.5 

45 

46 

1600.9 

67.8 

35.3 

o3.5 

72.2 

41.7 

11.9 

82.9 

54.6 

27.2 

2300.7 

46 

47 

02.0 

69.0 

36.5 

o4.6 

73.4 

42.9 

i3.i 

84.0 

55.8 

28.5 

02.0 

47 

48 

o3.i 

70.1 

37.6 

05.7 

74.5 

44.o 

i4.3 

85.2 

57.0 

29.7 

o3.2 

48 

49 

04.2 

71.2 

38. 7 

06.9 

75.7 

45.2 

i5.4 

86.4 

58.2 

30.9 

04.4 

49 

5o 

i6o5.4 

1672.3 

i739.9 

1808.0 

1876.8 

1946.4 

2016.6 

2087.6 

2159.4 

2232.1 

23o5.7 

5o 

5i 

o6.5 

73.4 

41.0 

09.2 

78.0 

47-5 

17.8 

88.8 

60.7 

33.3 

06.9 

5i 

52 

07.6 

74.5 

42.1 

io.3 

79.2 

48.7 

19.0 

90.0 

61.9 

34-6 

08.1 

5a 

53 

08.7 

75.7 

43.2 

11.4 

8o.3 

49.9 

20.2 

91.2 

63.i 

35.8 

09.4 

53 

54 

09.8 

76.8 

44-4 

12.6 

8i.5 

5i.o 

21.3 

92.4 

64-3 

37.0 

10.6 

54 

55 

10.9 

77-9 

45.5 

i3.7 

82.6 

52.2 

22.5 

93.6 

65.5 

38.2 

11. 8 

55 

56 

12.0 

79.0 

46.6 

14.9 

83.8 

53.4 

23.7 

94.8 

66.7 

39.4 

i3.i 

56 

57 

i3.i 

80.2 

47-8 

16.0 

84-9 

54.5 

24.9 

96.0 

67.9 

40.7 

i4.3 

57 

58 

l4-2 

8i.3 

48.9 

17.2 

86.1 

55.7 

26.0 

97.1 

69.1 

4i-9 

i5.5 

58 

59 

i5.4 

82.4 

5o.o 

i8.3 

87.2 

56.9 

27.2 

98.3 

70.3 

43.i 

16.8 

59 

Meridional    Parts. 


145 


LATITUDE. 

Mm 

36° 

37°   J  38° 

39° 

40° 

41° 

42°   |  43° 

44° 

45° 

46° 

Min. 

O 

23i8.o 

2392.6  2468.3 

2545.o 

2622.7 

2701.6 

2781.7  2863.1 

2945.8 

3o3o.o 

3n5.6 

O 

I 

19.2 

93.9 

69.5 

46.2 

24.0 

02.9 

83.i 

64-5 

47.2 

3i.4 

17.0 

1 

S 

20.5 

95.1 

70.8 

47-5 

25.3 

o4.3 

84-4 

65.8 

48.6 

32.8 

i8.5 

a 

3 

21.7 

96-4 

72.1 

48.8 

26.6 

o5.6 

85.8 

67.2 

5o.o 

34.2 

19.9 

3 

4 

23.0 

97-7 

73.4 

5o.i 

27.9 

06.9 

87.1 

68.5 

5i.4 

35.6 

21.4 

A 

5 

24.2 

98.9 

74.6 

5i.4 

29.2 

o8.3 

88.5 

70.0 

52.8 

37.0 

22.8 

5 

6 

25.4 

2400.2 

75.9 

52.7 

3o.5 

09.6 

89.8 

71.3 

54.2 

38.4 

24.2 

6 

7 

26.7 

01.4 

77.1 

54.o 

31.9 

10.9 

91.2 

72.7 

55.6 

39.8 

25.7 

7 

8 

27.9 

02.7 

78.5 

55.3 

33.2 

12.2 

92.5 

74.1 

57.0 

4i.3 

27.1 

8 

9 

29.1 

03.9 

79-7 

56.6 

34.5 

i3.5 

93.8 

75.4 

58.3 

42.7 

28.5 

9 

IO 

233o.4 

24o5.2 

2481.0 

2557.8 

2635.8 

2714.9 

2795.1 

2876.8 

2959.8 

3o44-i 

3i3o.o 

10 

II 

3i.6 

06.4 

82.2 

59.1 

37.i 

16.2 

96.5 

78.2 

61. 1 

45.5 

3i.5 

II 

12 

32.9 

O7.7 

83.5 

60.4 

38.4 

17.5 

97-9 

79.5 

62.5 

47.0 

32.9 

12 

i3 

34.1 

O9.O 

84-8 

61.7 

39.7 

18.9 

99.3 

80.9 

63.9 

48.4 

34.3 

13 

i4 

35.3 

10.2 

86.1 

63.o 

4i.o 

20.2 

2800.6 

82.3 

65.3 

49.8 

35.8 

i4 

i5 

36.6 

11. 5 

87.4 

64-3 

42.3 

21.5 

02.0 

83.7 

66.7 

5i.? 

37.2 

i5 

16 

37.8 

12.7 

88.6 

65.6 

43.6 

22.9 

o3.3 

85.o 

68.1 

5a.6 

38.7 

16 

»7 

39.0 

14.0 

89.9 

66.9 

44.9 

24.2 

04.7 

86.4 

69.5 

54.i 

4o.i 

17 

18 

4o.3 

l5.2 

91.2 

68.2 

46.3 

25.5 

06.0 

87.8 

70.9 

55.5 

4i.6 

18 

*9 

4i.5 

iG.5 

92.4 

69.5 

47-6 

26.8 

07.3 

89.1 

72.3 

56.9 

43.0 

J9 

20 

2342.8 

2417-8 

2493.7 

2570.7 

2648.9 

2728.2 

2808.8 

2890.5 

2973.7 

3o58.3 

3i44-5 

20 

21 

44.o 

19.0 

95.0 

72.0 

5o.a 

29.5 

IO.I 

91.9 

75.i 

59.7 

45.9 

21 

22 

45.3 

20.3 

96.3 

73.3 

5i.5 

3o.8 

II.4 

93.3 

76.5 

61.2 

47-4 

22 

23 

46.5 

21.5 

97.6 

74-6 

52.8 

32.2 

12.8 

94.7 

77-9 

62.6 

48.8 

23 

24 

47-7 

22.8 

98.8 

75.9 

54-1 

33.5 

i4.i 

96.0 

79.3 

64.o 

5o.3 

24 

25 

49-o 

24-"  25oo.i 

77.2 

55.5 

34.8 

i5.5 

97-4 

80.7 

65.4 

5i.7 

25 

26 

5o.2 

25.3      01.4 

78.5 

56.8 

36.2 

16.8 

98.8 

82.1 

66.9 

53.2 

26 

27 

5i.5 

26.5 

02.7 

79.8 

58.i 

37.5 

18.2 

2900.2 

83.5 

68.3 

54.6 

27 

28 

52.7 

27.8 

03.9 

81. 1 

59.4 

38.8 

19.5 

oi.5 

84-9 

69.7 

56.i 

28 

89 

54.o 

29.1 

o5.2 

82.4 

60.7 

4o.2 

20.9 

02.9 

86.3 

71.1 

57.5 

29 

3c 

2355.2 

243o.3  25o6.5 

2583-7 

2662.0 

274t.5 

2822.3 

2904.3 

2987.7 

3072.6 

3i5g.o 

3o 

3i 

56.5 

3i.6 

07.8 

85.o 

63.3 

42-9 

23.6 

05.7 

89.1 

74.0 

60.4 

3i 

32 

57.7 

32.9 

09.0 

86.3 

64.6 

44-2 

25. 0 

07.1 

90.5 

75.4 

61.9 

32 

33 

58.9 

34.i 

10.3 

87.6 

66.0 

45.5 

26.3 

08.4 

91.9 

76.9 

C3.3 

33 

34 

60.2 

35.4 

11.G 

88.9 

67.3 

46-9 

27.7 

09.7 

93.3 

78.3 

64.8 

34 

35 

61.4 

36.7 

12.9 

90.2 

68.6 

48.2 

29.0 

1 1.2 

94.7 

79-7 

6C.2 

35 

36 

62.7 

37.9 

l4*2 

91.5 

69.9 

49-5 

3o.4 

12.6 

96.1 

81. 1 

67.7 

36 

3? 

63.9 

39.2 

i5.4 

92.8 

71.2 

50.9 

3i.7 

i4-o 

97.5 

82.6 

69.1 

37 

38 

65.2 

4o.4 

16.7 

94.1 

72.5 

52.2 

33.i 

i5.3 

98.9 

84-o 

70.6 

38 

39 

66.4 

41.7 

18.0 

95.4 

73.9 

53.5 

34-5 

16.7 

3ooo.3 

85.4 

72.0 

39 

4o 

2367.6 

2443.o 

2519.3 

2596.7 

2675.2 

2754-9 

2835.8 

2918.1 

3ooi.8 

3086.9 

3i73.5 

4o 

4i 

68.9 

44.2 

20.5 

98.0 

76.5 

56.2 

37.2 

19.5 

o3.2 

88.3 

75.0 

4i 

42 

70.2 

45.5 

21.8 

99.3 

77-8 

57.6 

38.6 

20.9 

o4.6 

89.7 

76.4 

42 

43 

71.4 

46.8. 

23.1 

2600.5 

79.1 

58.9 

39.9 

22.3 

06.0 

91.2 

77-9 

43 

44 

72.6 

48.o 

24.4 

01.9 

8o.5 

60.2 

4i.3 

23.6 

07.4 

92.6 

79.3 

44 

45 

73.9 

49-3 

25.7 

o3.2 

81.8 

6i.5 

42.6 

25-0 

08.8 

94.0 

80.8 

45 

46 

75.. 

5o.6 

27.0 

04.5 

83.i 

62.9 

44-o 

26.4 

10.2 

95.5 

82.3 

46 

47 

76.4 

5i.8 

28.3 

o5.8 

84-4 

64.3 

45.4 

27.8 

1 1.6 

96.9 

83.7 

47 

48 

77.6 

53.i 

29.5 

07.1 

85. 7 

65.6 

46.7 

29.2 

1 3.o 

98.3 

85.2 

48 

49 

78.9 

54-3 

3o.8 

08.4 

87.1 

66.9 

48.1 

3o.6 

i4-4 

99-7 

86.6 

49 

5o 

j38o.i 

2455.6  2532.1 

2609.7 

2688.4 

2768.3 

2849.5  2932.0 

3oi5.8 

3ioi.2  3i88.i 

5o 

5i 

81.4 

56.9      33.4 

1 1.0 

89.7 

69.6 

5o.8      33.3 

17.2 

02.6      89.6 

5i 

52 

,82.6 

58.i      34.7 

12.3 

91.0 

71.0 

52.2 

34-7 

18.7 

o4.ij     91.0 

52 

53 

83.9 

59.41     36. 0 

i3.6 

92.3 

72.3 

53.5 

36.i 

20.1 

o5.6      92.5 

53 

54 

85.i 

60.7I     37.2 

i4-9 

93.7 

73.7 

54.9 

37.5         21.5 

07.0      94.0 

54 

55 

86.4 

61.9 

38.5 

16.2 

95.0 

75.0 

56.3 

38.9!     22.9 

08.4      95.4 

55 

56 

87.6 

63.2 

39.8 

17.5 

96.3 

76.3 

57.7 

4o.3;     24.3      09.8      96.9'   56 

57 

88.9 

64.5 

4i.i 

18.8 

97-6.     77.7      59.0,     4 1  -7,     25.7      1 1.2      98.4    57 

58 

90.2I     65.8 

42.4 

20.1 

99.0      79. i)      6o.5      43.1]     27.1       12.7      998    58 

59 

91.4,     67.0 

43.6 

21.4  2700.3!     80.4      61.7,     44-4      28.5      14.1  32oi.3    5^  j 

146 


Meridional   Parts. 


LATITUDE. 

Min. 

47° 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

Mia. 

O 

3202.7 

3291.5 

3382.1 

3474.5 

3568.8 

3665.2 

3763.8 

3864.6 

3968.0 

4073.9 

4182  6 

0 

I 

o4*2 

93.0 

83.6 

76.0 

70.4 

66.8 

65.4 

66.3 

69.7 

75.7 

84.5 

I 

2 

05.7 

94.5 

85.i 

77.6 

72.0 

08.4 

67.1 

68.0 

71.5 

77.5 

86.3 

2 

3 

07.1 

96.0 

86.7 

79.1 

73.6 

70.1 

68.8 

69.7 

73.2 

79.3 

88.1 

3 

4 

08.6 

97.5 

88.2 

80.7 

75.2 

71.7 

70.4 

71.5 

75.0 

8l.  T 

90.0 

4 

5 

10. 1 

99.0 

89.7 

82.3 

76.8 

73.3 

72.1 

73.2 

76.7 

82.9 

91.8 

5 

6 

ii.5 

33oo.5 

91.3 

83.8 

784 

75.0 

73.7 

74.9 

78.4 

84.7 

93.7 

6 

7 

i3.o 

02.0 

92.8 

85.4 

79-9 

76.6 

75.4 

76.6 

80.2 

86.4 

95.5 

7 

8 

i4-5 

o3.5 

94.3 

87.0 

8i.5 

78.2 

77.1 

78.3 

82.0 

88.2 

97.3 

8 

9 

15.9 

o5.o 

95.8 

88.5 

83.i 

79.8 

78.7 

80.0 

83.7 

90.0 

99.2 

9 

IO 

3217.4 

33o6.5" 

3397.4 

3490.1 

3584-7 

368i.5 

3780.4 

3881.7 

3985.4 

4091.8 

4201.0 

10 

ii 

18.9 

08.0 

98.9 

91.6 

86.3 

83.i 

82.1 

83.4 

87.2 

93.6 

02.9 

11 

12 

20.3 

09.5 

34oo.4 

93.2 

87.9 

84-7 

83.7 

85.i 

88.9 

95.4 

04.7 

12 

i3 

21.8 

11. 0 

02.0 

-$73 

89.5 

86.4 

85.4 

86.8 

90.7 

97.2 

06.6 

i3 

i4 

23.3 

12.5 

o3.5 

91.1 

88.0 

87.1 

88.5 

92.5 

99.0 

08.4 

14 

i5 

24.8 

14.0 

o5.o 

97-9 

92.7 

89.6 

88.8 

90.2 

94.2 

4100.8 

io.3 

i5 

16 

26.2 

i5.5 

06.6 

99.4 

94-3 

91.3 

90.4 

92.0 

96.0 

02.6 

12. 1 

16 

*7 

27.7 

17.0 

08.1 

35oi.o 

95.9 

92.9 

92.1 

93.7 

97-7 

o4.4 

i4-o 

17 

18 

29.2 

i8.5 

09.6 

02.6 

97.5 

94.5 

93.8 

95.4 

99.5 

06.2 

i5.8 

18 

*9 

30.7 

20.0 

11. 1 

o4-i 

99.1 

96.2 

95.5 

97.1 

4001.2 

08.0 

17.7 

19 

20 

3232.1 

3321.5 

3412.7 

35o5-7 

3600.7 

3697.8 

3797.1 

3898.8 

4oo3.o 

4109.8 

4219.5 

20 

21 

33.6 

23.0 

14.2 

07.3 

02.3 

99.4 

98.8 

3900.5 

o4-7 

11.6 

21.4 

21 

22 

35.i 

24.5 

i5.7 

08.8 

03.9 

3701. 1 

38oo.5 

02.2 

o6.5 

1 3.4 

23.2 

22 

23 

36.6 

26.0 

17.3 

10.4 

o5.5 

02.7 

02.2 

04.0 

o8.3 

l5.2 

25.1 

23 

24 

38.o 

27.5 

18.8 

12.0 

07.1 

o44 

o3.8 

05.7 

10. 0 

17.1 

27.O 

24 

25 

39.5 

29.0 

20.4 

1 3.5 

08.7 

06.0 

o5.5 

07.4 

11.8 

18.9 

28.8 

25 

26 

41.0 

3o.6 

21.9 

i5.i 

io.3 

07.6 

07.2 

09.1 

i3.5 

20.7 

3o.6 

26 

27 

42.5 

32.1 

23.5 

16.7 

11.9 

09.3 

08.9 

10.8 

i5.3 

22.5 

32.5 

27 

28 

44-0 

33.6 

25. 0 

i8.3 

i3.6 

10.9 

io.5 

12.5 

17.1 

24.3 

34-4 

28 

29 

45.4 

35.i 

26.5 

19.8 

i5.i 

12.6 

12.2 

14.3 

18.8 

26.1 

36.2 

29 

3o 

3246.9 

3336.6 

3428.0 

3521.4 

3616.7 

3714.2 

38i3-9 

3916.0 

4020.6 

4127.9 

4238.1 

3o 

Ji 

48.4 

38.i 

29.6 

23.0 

18.4 

i5.8 

1 5.6 

17.7 

22.4 

29.7 

4o.o 

3i 

32 

49.9 

39.6 

3i.i 

24.6 

20.0 

17.5 

17.3 

19.4 

24-1 

Si  .5 

4i.8 

32 

33 

5i.4 

41.1 

32.7 

26.1 

21.6 

19.1 

18.9 

21.2 

25.9 

33.3 

43.7 

33 

34 

52.8 

42.6 

34.2 

27.7 

23.2 

20.8 

20.6 

22.9 

27.7 

35.2 

45.5 

34 

35 

54.3 

44-1 

35.8 

29.3 

24.8 

22.4 

22.3 

24-6 

29.4 

37.0 

47-4 

35 

36 

55.8 

45.7 

37.3 

3o.8 

26.4 

24.1 

24.0 

26.3 

3l.2 

38.8 

49.3 

36 

37 

57.3 

47.2 

38.8 

32.4 

28.0 

25.7 

25.7 

28.1 

33.0 

4o.6 

5i.i 

37 

38 

58.8 

48.7 

4o.4 

34.o 

29.6 

27.4 

27.4 

29.8 

34.8 

42.4 

53.o 

38 

39 

6o.3 

5o.2 

41.9 

35.6 

3i.3 

29.0 

29.1 

3i.5 

36.5 

44-2 

54,9 

39 

4o 

3261.7 

3351.7 

3443.5 

3537.1 

3632.8 

3730.7 

383o.8 

3933.2 

4o38.3 

4 1 46. 1 

4256.7 

4o 

4i 

63.2 

53.2 

45.o 

38.7 

344 

32.3 

32.4 

35.o 

4o.i 

47-9 

58.6 

.4i 

4a 

64-7 

54.7 

46.6 

4o.3 

36.i 

34.o 

34.i 

36.7 

41.8 

49-7 

6o.5 

42 

43 

66.2 

56.2 

48.i 

41.9 

37.7 

35.6 

35.8 

38.4 

43.6 

5i.5 

62.3 

43 

44 

67.7 

57.8 

49-7 

43.5 

39.3 

37.3 

37.5 

4o.2 

45.4 

53.4 

64.2 

44 

45 

69.2 

59.3 

5l.2 

45.o 

40.9 

38.9 

39.2 

4l-9 

47.2 

55.2 

66.1 

45 

40 

70.7 

60.8 

52.8 

46.6 

42.5 

4o.6 

40.9 

43.6 

49.0 

57.0 

68.0 

46 

47 

72.1 

62.3 

54.3 

48.2 

44.i 

42.2 

42.6 

45.4 

50.7 

58.8 

69.8 

47 

48 

73.6 

63.8 

55.8 

49.8 

45.8 

43.9 

44.3 

47.1 

52.5 

60.7 

71.7 

48 

49 

75.1 

65.4 

57-4 

5i.4 

47-4 

45.5 

46.o 

48.8 

54.3 

62.5 

73.6 

49 

5o 

3276.6 

3366-9 

3458-9 

3553.0 

3649-o 

3747-2 

3847-7 

3950.6 

4o56.i 

4i64-3 

4275.5 

5o 

5i 

78.1 

68.4 

6o.5 

54.6 

5o.6 

48.8 

49-4 

52.3 

57.8 

66.1 

77-4 

5i 

52 

79.6 

69.9 

62.0 

56.i 

52.2 

5o.5 

5i.i 

54.o 

59.6 

68.0 

79.2 

52 

53 

81. 1 

71.4 

63.6 

57.7 

53.8 

52.1 

52.8 

55.8 

61.4 

69.8 

81.1 

53 

54 

82.6 

73.0 

65.2 

59.3 

55.5 

53.8 

54-4 

57.5 

63.2 

71.6 

83.o 

54 

55 

84.1 

74.5 

66.7 

60.9 

57-i 

55.5 

56.i 

59.3 

65.o 

73.5 

84-9 

55 

56 

85.6 

76.0 

68.3 

62.5 

58-7 

57.1 

57.8 

61.0 

66.8 

75.3 

86.8 

56 

57 

87.1 

77.5 

69.8 

64.0 

6o-3 

58.8 

59.5 

62.7 

68.5 

77.1 

88.6 

57 

58 

88.5 

79.0 

71.4 

65.6 

61.9 

6o.4 

61.2 

64-5 

70.3 

79.0 

90.5 

58 

j59 

90.0 

80.6 

73.0]  67.2 

63-6   62.1 

62.9 

66.2 

72.1 

80.8 

92.4 

59 

Merilional    Farts. 


147 


LATITUDE. 

Mjl 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

Min. 

o 

4294.3 

4409.1 

4527.4 

4649.2 

4775.0 

4904.9 

5039.4 

5i78.8 

5323.5 

5474.0 

563o.8 

O 

I 

96.2 

11. 1 

29.4 

5i.3 

77.1 

07.1 

4i-7 

81.2 

26.0 

76.6 

33.5 

1 

a 

98.1 

i3.o 

3i.4 

53.4 

79.3 

09.4 

44.0 

83.5 

28.4 

79.1 

36.2 

3 

3 

43oo.o 

1 5.o 

33.4 

55.4 

81.4 

11.6 

46.3 

85.9 

30.9 

81.7 

38.8 

3 

4 

01.9 

16.9 

35.4 

57.5 

83.5 

i3.8 

48.6 

88.3 

33.4 

84-3 

4i.5 

4 

5 

03.7 

18.9 

37.4 

59.6 

85.6 

16.0 

50.9 

90.7 

35.8 

86.9 

44-2 

5 

6 

o5.6 

20.8 

39.4 

61.6 

87.8 

18.2 

53.1 

93.1 

38.3 

89.4 

46.9 

e 

7 

07.5 

22.8 

4i-4 

63.7 

89.9 

20.4 

55.4 

95.4 

4o.8 

92.0 

49-6 

7 

8 

09.4 

24-7 

43.4 

65.8 

92. i|  22.6 

57.7 

97.8 

43.2 

94.5 

52.3 

8 

9 

ii.3 

26.7 

45.4 

67.8 

94.2 

24.8 

60.0 

5200.2 

45.7 

97.1 

54.9 

9 

IO 

43i3.2 

4428.6 

4547-4 

4669.9 

4796.3 

4927.0 

5o62.3 

5202.6 

5348.2 

5499.7 

5657.6 

10 

ii 

i5.i 

3o.6 

49.4 

72.0 

98.5 

29.2 

64-6 

04-9 

5o«7 

55o2.3 

6o.3 

11 

12 

17.0 

32.5 

5i.4 

74-i 

4800.6 

3i.5 

66.9 

O7.3 

53.i 

04.9 

63.o 

12 

i3 

18.9 

34.5 

53.5 

76.1 

02.8 

33.7 

69.2 

O9.7 

55.6 

07.4 

65.7 

i3 

i4 

20.8 

36.4 

55.5 

78.2 

04.9 

35.9 

71.5 

12. 1 

58.i 

10. 0 

68.4 

i4 

i5 

22.7 

38.4 

57.5 

8o.3 

07.1 

38.i 

73.8 

l4-5 

60.6 

12.6 

71. 1 

i5 

16 

24.6 

4o.3 

59.5 

82.4 

09.2 

4o.3 

76.1 

16.9 

63.i 

1 5.2 

73.8 

16 

*7 

26.5 

42.3 

6i.5 

84-5 

11.4 

42.6 

78.4 

19.3 

65.6 

17.8 

76.5 

17 

18 

28.4 

44-2 

63.5 

86.5 

i3.5 

44-8 

80.7 

21.6 

68.0 

20.4 

79.2 

18 

*9 

3o.3 

46.2 

65.6 

88.6 

i5.7 

47.0 

83.o 

24.0 

70.5 

23.0 

81.9 

'9 

20 

4332.2 

4448.2 

4567.6 

4690.7 

4817.8 

4949.2 

5o85.3 

5226.4 

5373.0 

5525.6 

5684-6 

20 

21 

34-1 

5o.i 

69.6 

92.8 

20.0 

5i.5 

87.6 

28.8 

75.5 

28.1 

87.3 

21 

22 

36.o 

52.1 

71.6 

94.9 

22.1 

53.7 

90.0 

3l.2 

78.0 

30.7 

90.0 

22 

23 

37.9 

54.i 

73.6 

97.0 

24-3 

55.9 

92.3 

33.6 

8o.5 

33.3 

92.7 

23 

24 

39.8 

56.o 

75.7 

99.1 

26.4 

58.2 

94.6 

36.0 

83.o 

35.9 

95.5 

24 

25 

4i.8 

58.o 

77-7 

4701. 1 

28.6 

60.4 

96.9 

38.4 

85.5 

38.6 

98.2 

25 

26 

43.7 

60.0 

79-7 

o3.2 

3o.8 

62.6 

99.2 

4o.8 

88.0 

4l.2 

5700.9 

26 

27 

45.6 

61.9 

81.7 

o5.3 

32.9 

64-9 

5ioi.5 

43.2 

90.5 

43.8 

o3.6 

27 

28 

47-5 

63.9 

83.8 

07.4 

35.i 

67.1 

o3.8 

45.7 

93.0 

46.4 

o6.3 

28 

29 

49.4 

65.9 

85.8 

09.5 

37.3 

69.4 

06.2 

48.1 

95.5 

49.0 

09.1 

29 

3o 

435i.3 

4467.8 

4587.8 

4711.6 

4839.4 

4971.6 

5io8.5 

525o.5 

5398.0 

555i.6 

5711.8 

3o 

3i 

53.2 

69.8 

89.9 

i3.7 

4i.6 

73.8 

10.8 

52.9 

54oo.5 

54.2 

i4-5 

3i 

32 

55.i 

71.8 

91.9 

i5.8 

43.8 

76.1 

i3.i 

55.3 

o3.o 

56.8 

17.3 

32 

33 

57.i 

73.7 

93.9 

17.9 

45.9 

78.3 

i5.5 

57.7 

o5.5 

59.4 

20.0 

33 

34 

59.0 

75.7 

96.0 

20.0 

48.i 

80.6 

17.8 

60.1 

08.1 

62.1 

22.7 

34 

35 

60.9 

77-7 

98.0 

22.1 

5o.3 

82.8 

20.1 

62.6 

10.6 

64-7 

25.5 

35 

36 

62.8 

79-7 

4600.0 

24.2 

52.4 

85.i 

22.4 

65.o 

i3.i 

67.3 

28.2 

36 

37 

64-7 

81.6 

02.1 

26.3 

54.6 

87.3 

24.8 

67.4 

1 5.6 

69.9 

30.9 

37 

38 

66.7 

83.6 

o4- 1 

28.4 

56.8 

89.6 

27.1 

69.8 

18.1 

72.6 

33.7 

38 

39 

68.6 

85.6 

06.1 

3o.5 

59.0 

91.8 

29.4 

72.2 

20.6 

75.2 

36.4 

39 

4o 

4370.5 

4487.6 

4608.2 

4732.6 

486i.i 

4994.1 

5i3i.8 

5274.7 

5423.2 

5577.8 

5739.2 

4o 

4i 

72.4 

89.6 

10.2 

34.7 

63.3 

96.3 

34.i 

77.1 

25.7 

80.4 

4i-9 

4i 

42 

74.3 

91.5 

12.3 

36.8 

65.5 

98.6 

36.5 

79.5 

28.2 

83.i 

44.7 

4a 

43 

76.3 

93.5 

i4.3 

39.0 

C7.7 

5ooo.8 

38.8 

82.0 

3o.8 

85.7 

47-5 

43 

44 

78.2 

95.5 

1G.4 

4i.i 

69.9 

o3.i 

4i.i 

84-4 

33.3 

88.4 

5o.2 

44 

45 

80.1 

97.5 

18.4 

43.2 

72.0 

o5.4 

43.5 

86.8 

35.8 

91.0 

52.9 

45 

46 

82.1 

99.5 

20.5 

45.3 

74.2 

07.6 

45.8 

89.3 

38.4 

93.6 

55.7 

46 

47 

84.o 

43oi.5 

22.5 

47-4 

76.4 

09.9 

48.2 

91.7 

40.9 

96.3   58.5 

47 

48 

85.9 

o3.4 

24.6 

49-5 

78.6 

12.2 

5o.5 

94.1 

43.4 

98.9 

61.2 

t^> 

49 

87.8 

o5.4 

26.6 

5i.G 

80.8 

i4-4 

52.9 

96.6 

46.o 

56oi.6 

64.o 

49 

5o 

4389.8 

4507.4 

4628.7 

4753.7 

4883.o'5oi6.7 

5i55.2 

5299.0 

5448.5 

56c>4.2 

5766.8 

5o 

5i 

91.7 

09.4 

30.7 

55.9 

85.2 

18.9 

57.6 

53oi.5 

5i.o 

06.9 

69.5 

5i 

52 

»  93.6 

11.4 

32.8 

58.o 

87.4 

21.2 

59.9 

03.9 

53.6 

09.5 

72.3 

52 

53 

95.6 

i3.4 

34.8 

60.1 

89.5 

2  3.5 

62.3 

o6.3   56.1 

12.2 

75.i 

53 

54 

97.5 

i5.4|  3G.9 

62.2 

91.7 

25.^ 

64-6 

08.8   58.7 

14.8 

77-9 

54 

55 

99.4 

17.41  39.0 

64-4 

93.9 

28.0 

67.0 

11.2   61.2 

17.5 

80.6 

55 

56 

44oi.4 

19.4,  4i-o 

66.5 

96.1 

3o.3 

69.4 

1 3.7 

63.8 

20.2   83.4 

56 

57 

o3.3 

21.4 

43.0 

68.6 

98.3 

32.6 

7'-7 

1  &  1 

66.3   22. g:   86.2 

57 

58 

o5.3 

23.4 

45.1 

7o.7'4<;oo.5 

34-9 

74-1 

18.6:  68.9J  25.5;  89.0 

58 

59 

07.2 

25.4 

47.2 

72.9|  02.7 

37. j   76.4 

2 1. 1   71.4   28.2 

91.8 

5, 

148 


Meridional    Parts. 


~ — ---   ._.  .1.-  i 

LATITUDE. 

Mia 

69° 

70° 

71° 

72° 

73° 

74° 

»  O 

76° 

77° 

78° 

79° 

Mill. 

o 

5794.6 

5965.9 

6145.7 

£334.8 

6534-4 

6745.7 

6970.3 

7210. 1 

7467.2  7744.6 

8045.7 

0 

I 

97-4 

68.8 

48.8 

38.i 

37.8 

49-4 

74.2 

14.2 

71.7 

49-4 

5i.o 

I 

2 

58oo.i 

71.8 

51.9 

4i.3 

4i.3 

53.o 

78.I 

i8.3 

76.1 

54.2 

56.2 

2 

3 

02.9 

74-7 

54.9 

44-6 

44.7 

56.6 

81.9 

22.5 

80.6 

5g.o 

6i.5 

3 

4 

05.7 

77.6 

58.o 

4;.8 

48.i 

6o.3 

85.8 

26.6 

85.o 

63.9 

66.7 

4 

5 

o8.5 

80.6 

61. 1 

5i.i 

5i.6 

63.9 

89.7 

3o.8 

89.5 

68.7 

72.0 

5 

6 

n. 3 

83.5 

64.2 

54.3 

55.o 

67.6 

93.6 

35.o 

94.0 

73.5 

77.3 

6 

7 

l4-2 

86.4 

67.3 

57.6 

58.5 

71.2 

97.5 

39.1 

98.5 

78.4 

82.6 

7 

8 

1.7.0 

89.4 

70.4 

60.8 

61.9 

74.9 

7001.4 

43.3 

75o3.o 

83.3 

87.9 

8 

9 

19.8 

92.3 

73.5 

64.1 

65.3 

78.5 

o5.3 

47-5 

07.4 

88.1 

93.2 

9 

IO 

5822.6 

5995.3 

6176.6 

6367.4 

6568.8 

6782.2 

7009.2 

7251.7 

7511.9 

7793.0 

8098.5 

10 

ii 

25.4 

98.2 

79-7 

70.6 

72.3 

85.9 

i3.i 

55.8 

i6.5 

97-9 

8io3.8 

11 

12 

28.2 

6001.2 

82.8 

73.9 

75.7 

89.6 

17.0 

60.0 

21.0 

7802.8 

09.2 

12 

i3 

3i.o 

04.1 

85.9 

77.2 

79.2 

93.2 

20.9 

64.2 

25.5 

07.7 

i4.5 

i3 

i4 

33.8 

07.1 

89.0 

80.4 

82.6 

.  96-9 

24.8 

68.4 

3o.o 

12.6 

19.9 

14  . 

i5 

36.7 

10. 0 

92.1 

83.7 

86.1 

6800.6 

28.8 

72.6 

34.5 

i7.5 

25.2 

i5 

16 

39.5 

i3.o'  9S.2 

87.0 

89.6 

o4-3 

32.7 

76.8 

39.1 

22.4 

3o.6 

16 

*7 

42.3 

16.0 

98.3 

90.3 

93.0 

08.0 

36.6 

81. 1 

43.6 

27.3 

36.o 

n 

18 

45.i 

18.9 

6201.4 

93.6 

96.5 

11.6 

4o.6 

-85.3 

48.i 

32.2 

4i-3 

18 

l9 

48.0 

21.9 

o4.5 

96.9 

6600.0 

i5.4 

44-5 

89.5 

52.7 

37.2 

46.7 

*9 

20 

585o.8 

6024.9 

6207.7 

6400.2 

66o3.5 

6819. 1 

7048.5 

7293.7 

7557.3 

7842.1 

8i52.i 

20 

21 

53.6 

27.8 

10.8 

o3.4 

07.0 

22.8 

52.4 

98.0 

61.8 

47.1 

57.5 

21 

22 

56.5 

3o.8 

13.9 

06.7 

io.5 

26.5 

56.4 

7302.2 

66.4 

52. 0 

62.9 

22 

23 

59.3 

33.8 

17.0 

10. 1 

i4-o 

3o.2 

6o.3 

06.4 

71.0 

57.0 

68.4 

23 

24 

62.2 

36.8 

20.2 

1 3.4 

17.5 

33.9 

64.3 

10.7 

75.5 

61.9 

73.8 

24 

25 

65.o 

39.8 

23.3 

16.7 

21.0 

37.6 

68.3 

i5.o 

80.1 

66.9 

79.2 

25 

26 

67.8 

42.7 

26.5 

20.0 

24.5 

4i.3 

72.2 

19.2 

84-7 

71.9 

84-7 

26 

27 

70.7 

45.7 

29.6 

23.3 

28.0 

45.i 

76.2 

23.5 

89.3 

76.9 

90.1 

27 

28 

73.5 

48.7 

32.7 

26.6 

3i.5 

48.8 

80.2 

27.7 

93.9 

81.9 

95.6 

28 

29 

76.4 

5i.7 

35.9 

29.9 

35.o 

52.5 

84.2 

32.o 

98.5 

86.9  8201. 1 

29 

3o 

5379.2 

6o54-7 

6239.0 

6433.3 

6638.5 

6856.3 

7088.2 

7336.3 

7603.2 

7891.9  8206.6 

3o 

3i 

82.1 

57.7 

42.2 

36.6 

42.1 

60.0 

92.2 

4o.G|  07.8 

96. 9|  12. 1 

3i 

32 

85.o 

60.7 

45.3 

39.9 

45.6 

63.8 

96.2 

44-9 

12.4 

7902.0 

17.6 

32 

33 

87.S 

63.7 

48.5 

43.2 

49.1 

67.5 

7100.2 

49.2 

17.0 

07.0 

23.1 

33 

34 

90.7 

66.7 

5i.7 

46.6 

52.6 

71.3 

04.2 

53.5 

21.7 

12.0 

28.6 

34 

35 

93.6 

69.7 

54.8 

49.9 

56.2 

75.0 

08.2 

57.8 

26.1 

17.1 

34-1 

35 

36 

96.4 

72.7 

58.o 

53.3 

59.7 

78.8 

12.2 

62.1 

3i.o 

22.1 

39.7 

36 

37 

99.3 

75.7 

61.2 

56.6 

63.3 

82.6 

i6.3 

66.4 

35.6 

27.2 

45.2 

37 

38 

5902.2 

78.8 

64-3 

60.0 

66.8 

86.3 

20.3 

70.7 

4o.3 

32.3 

5o.8 

38 

39 

o5.o 

81.8 

67.5 

63.3 

70.4 

90.1 

24-3   75.1 

45.o 

37.3 

56.3 

39 

4o 

5907.9 

6084.8 

6270.7 

6466.7 

6673.9 

6893.9 

7128.4  7379.4 

7649.7 

7942.4 

87.61.9 

4o 

4i 

10.8 

87.8 

73.9 

70.0 

77-4 

97-7 

32.4   80.7 

54.3 

47-5 

67.5 

4i 

42 

i3.7 

90.8 

77.1 

73.4 

81.0 

6901.5 

36.4 

88.1 

59.0 

52.6 

73.i 

'42 

43 

16.6 

93.9 

80.2 

76.7 

84-6 

o5.3 

4o.5 

92.4 

63.7 

57.7 

78.6 

43 

44 

19.4 

96.9 

83.4 

80.1 

88.2 

09.1 

44-5 

96.8 

68.4 

62.8 

84-3 

44 

45 

22.3 

99.9 

86.6 

83.5 

91.7 

12.9 

48.6 

7401. 1 

73.2 

68.0 

S9.9 

45 

46 

25.2 

6io3.o 

89.8 

86.9 

95.3 

16.7 

52.7 

o5.5 

77-9 

73.i 

95.5 

46 

47 

28.1 

06.0 

93.0 

90.2 

98.9 

20.5 

56.7 

09.9 

82.6 

78.2 

83oi.i 

47 

48 

3i.o 

09.0 

96.2 

93.6 

6702.5 

24.3 

60.8 

i4-3 

87.3 

83.4 

06.7 

48 

49 

33.9 

12. 1 

99.4 

97.0 

06.1 

28.1 

64-9 

18.6 

92.1 

88.5 

12.4 

49 

5o 

5936.8 

6n5.i 

63o2.6 

65oo.4 

6709.7 

6931.9 

7169.0 

7423.0 

7696.8 

7993.7 

83i8.i 

5o  j 

5i 

39.7 

18.2 

o5.8 

o3.8 

13.2 

35.7 

73.i 

27.4 

7701.5 

98.9 

23.8 

5i 

52 

42.6 

21.2 

09.1 

07.2 

16.8 

93.6 

77.2 

3i.8 

o6.3 

8oo4-o 

29-4 

b-2   1 

53 

45.5 

24.3 

12.3 

10.6 

20.4 

43.4 

81.2 

36.2 

ii.i 

09.2 

35.i 

53  ' 

54 

48.4 

27.3 

i5.5 

14.0 

24.0 

47.2 

85.3 

4o.6 

i5.8 

i4.4 

4o.8 

54  j 

55 

5i.3 

3o.4 

18.7 

17.4 

27.7 

5i.i 

89.5 

45.i 

20.6 

19.6 

46.5 

55  | 

56 

54.2 

33.4 

21.9 

20.8 

3i.3 

54.9 

93.6 

49.5 

25.4 

24.8 

52.2 

56  ! 

57 

57.2 

36.5 

25.1 

24.2 

34.9 

58.8 

97-7 

53.9 

30.2 

3o.o 

58.o 

57 ; 

58 

60.1 

39.6 

28.4 

27.6 

38.5 

62.6 

7201.8 

58.3 

35.o 

35.2 

63.7 

58 

59 

63.o 

42.6 

3i.6 

3i.o 

42.1 

66.5 

o5.6   62.8   39.8 

4o.5 

69.4 

59  j 

Corrections    to    Middle    Latitude. 


141' 


Kid. 
Lat. 

DIFFERENCE  OF  LATITUDE. 

1° 

23 

3° 

•1° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17c 

18° 

19° 

20° 

o 

i5 

/ 
0 

1 

/ 
2 

/ 
3 

5 

7 

9 

12 

i5 

18  122 

26 

-t 
3i 

36 

4i 

47 

/ 

52 

59 

65 

72 

16 

0 

1 

2 

3 

4 

6 

9 

11 

i4 

18I21 

25 

3o 

34 

39 

44 

5o 

56 

62 

69 

»7 

0 

1 

2 

3 

4 

6 

8 

1 1 

i4 

17 

20 

24 

28 

33 

38 

43 

48 

54 

60 

66 

18 

0 

1 

3 

4 

6 

8 

10 

i3 

16 

20 

23 

27 

32 

36 

4i 

46 

52 

58 

64 

J9 

0 

1 

3 

4 

6 

8 

10 

i3  16 

'9 

22 

26 

3o 

35 

4o 

45 

5o 

56 

61 

20 

0 

1 

2  1  4 

5 

7 

10  12 

i5 

18 

22 

25 

29 

34 

38 

43 

48 

54 

60 

21 

0 

1 

2  4 

5 

7 

9 

12 

i5 

18 

21 

25 

29 

33 

37 

42 

47 

52 

58 

22 

0 

1 

2 

4 

5 

7 

9 

12 

i4 

17 

21 

24 

28 

32 

36 

4i 

46 

5i 

56 

23 

0 

1 

2 

3 

5 

7 

9 

1 1 

i4 

*7 

20 

23 

27 

3i 

35 

4o 

45 

5o 

55 

24 

0 

1 

2 

3 

5 

7 

9 

1 1 

i4 

16 

20 

23 

27 

3i 

35 

39 

44 

49 

54 

25 

0 

-* 

2 

3 

5 

7 

9 

1 1 

i3 

16 

J9 

23 

26 

3o 

34 

39 

43 

48 

53 

26 

0 

1 

2 

3 

5 

6 

8 

II 

i3 

16 

*9 

22 

26 

3o 

34 

38 

42 

47 

52 

27 

0 

1 

2 

3 

5 

6 

8 

II 

i3 

16 

19 

22 

25 

29 

33 

37 

42 

47 

52 

28 

0 

1 

2 

3 

5 

6 

8 

10 

i3 

16 

18 

22 

25 

29 

33 

37 

4i 

46 

5: 

29 

0 

1 

2 

3 

5 

6 

8 

10 

i3 

i5 

18 

21 

25 

28 

32 

37 

4i 

46 

5i 

3o 

0 

1 

2 

3 

5 

6 

8 

10 

i3 

i5 

18 

21 

25 

28 

32 

36 

4i 

45 

5o 

3i 

0 

1 

2 

3 

5 

6 

8 

10 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

5o 

32 

0 

a 

2 

3 

4 

6 

8 

10 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

5o 

33 

0 

0 

2 

3 

4 

6 

8 

10 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

49 

34 

0 

0 

2 

3 

4 

6 

8 

10 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

49: 

35 

0 

0 

2 

3 

4 

6 

8 

10 

12 

i5 

18 

21 

24 

28 

92 

36 

4o 

45 

49 

36 

0 

2 

3 

4 

6 

8 

10 

1 2 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

49 

3? 

0 

2 

3 

4 

6 

8 

10 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

49 

38 

0 

2 

3 

4 

6 

8 

10 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

5o 

39 

0 

2 

3 

4 

6 

8 

10 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

5o 

4o 

0 

2 

3 

5 

6 

8 

10 

i3 

i5 

18 

21 

25 

28 

32 

36 

4i 

45 

5o 

4i 

0 

2 

3 

5 

6 

8 

10 

i3 

i5 

18 

21 

25 

28 

32 

37 

4i 

46 

5l; 

42 

<» 

2 

3 

5 

6 

8 

10 

i3 

i5 

18 

22 

25 

29 

33 

37 

4i 

A6 

5n 

43  1 

<> 

2 

3 

5 

6 

8 

10 

i3 

16 

18 

22 

25 

29 

33 

37 

42 

46 

52' 

44 

0 

2 

3 

5 

6 

8 

10 

i3 

16 

!9 

22 

25 

29 

33 

38 

42 

47 

52 

45 

0 

2 

3 

5 

6 

8 

i3 

16 

x9 

22 

26 

3o 

34 

38 

43 

48 

53 

46 

0 

2 

3 

5 

6 

8 

i3 

16 

l9 

22 

2G 

3o 

34 

38 

43 

48 

53 

47 

0 

2 

3 

5 

7 

9 

i3  16 

!9 

23 

26 

3o 

35 

39 

44 

49 

54 

48 

0 

2  ^ 

3 

5   7 

9 

i4; 17  20 

23 

27 

3i 

35 

4o 

44 

5o 

55 

49 

0 

2 

3 

5 

7 

9 

i4  17 

20 

23 

27 

3i 

36 

4o 

45 

5o 

56 

5o 

0 

2 

4 

5 

7 

9 

i4 

17 

20 

24 

28 

32 

36 

4i 

46 

5i 

57 

5i 

0 

2 

4 

5 

7 

9 

12 

i4 

17 

21 

24 

28 

32 

37 

42 

47 

52 

58 

52 

0 

2 

4 

5 

7 

9 

12 

i5 

18 

21 

25 

29 

33 

38 

43 

48 

53 

59 

53 

0 

2 

4 

5 

7 

10 

12 

i5 

18 

21 

25 

29 

34 

38 

43 

49 

54 

60 

54 

0 

2 

4 

5 

7 

10 

12 

i5 

18 

22 

26 

3o 

34 

39 

44 

5o 

56 

62 

55 

0 

2 

4 

6 

8 

10 

i3 

16  19 

22 

26 

3i 

35 

4o 

45 

5i 

5? 

63 

56 

0 

3 

4 

6 

8 

10 

i3 

1 G  1 9 

2  3 

27 

3 1 

36 

4i 

46 

52 

58 

65 

57 

0 

3 

4 

6 

8 

10 

i3 

iG  20 

24 

28 

32 

37 

42 

48 

54 

60 

66 

5d 

0 

2 

O 

4 

6 

8 

1 1 

i4 

17  20 

24 

28 

33 

38 

43 

49 

55 

61 

68 

59 

0 

2 

3 

4 

6 

8 

1 1 

i4 

17  21 

25 

29 

34 

39 

45 

5o 

5? 

63 

70 

60 

0 

2 

3 

4 

6 

9 

1 1 

i4 

2G 

3o 

35 

4o 

46" 

52 

58 

65 

72 

6! 

0 

2 

3 

5 

7 

9 

12 

i5 

,8  22 

26 

3i 

3G 

42 

47 

53 

60 

67 

75 

62 

0 

2 

3 

5 

7 

9 

12 

i5 

l9  23 

27 

32 

37 

43 

49 

55 

62 

70 

77 

63 

0 

2 

3 

5 

7 

10 

1  2 

16 

20  24 

28 

33 

39 

44 

5i 

57 

64 

72 

80 

64 

0 

2 

3 

5 

7 

10 

i3 

16 

20  24 

29 

34 

4o 

46 

52 

59 

C'7 

75 

83 

05 

fi 

2 

3 

5 

7 

10 

1 3 

17 

21  ,  25 

3o 

36 

4i 

48 

54 

62 

69 

7* 

86 

66 

0 

2 

3 

5 

8 

1 1 

i4 

18 

22  '  26 

32 

37 

43 

5o  ">7 

64 

72 

81 

90 

67 

<< 

2 

4 

6 

8 

1 1 

i4 

iS 

23  28 

33 

39 

45 

67 

76 

85 

94 

68 

0 

2 

4 

6 

8 

12 

i5 

'9 

24  29 

34 

4o 

47 

r>4  62 

7'1 

79 

^ 

99 

69 

0 

2 

4 

6 

9 

12 

16 

20 

25  j  3o 

36 

42 

49 

57  65 

74 

8  ; 

9j 

104 

70 

0 

2 

4 

6 

9 

i3 

16 

21 

26  32 

38 

44 

52 

60  68 

7* 

NS 

98 

!  TO  j 

71 

0 

2 

4 

7 

i<> 

i3 

'7 

22 

27  33 

4o 

47 

55 

63  72  - 

93 

io4 

ll6| 

72 

0 

3 

5 

7 

10 

i4 

18 

23 

2n  15 

1 

42 

49 

58  67 

98 

[Hi 

^\ 

- 

150       Logarithms    for    computing    Compound    Interest. 


In  computing  compound  interest  for  long  periods  of  time,  it  is  necessary  to  have 
the  following  logarithms  to  more  than  six  places. 


Number. 


Logarithm. 


Number. 


Logarithm. 


I .0025 

I  .oo5o 
1 .0075 
I .0100 

I.OI25 

1 .oi5o 

1 .0175 

1 .0200 

1 .0225 

1 .o25o 

1 .0275 

o3oo 

o325 

o35o 

0375 

o4oo 


.00108 
.00216 
.oo324 
.00432 
.00539 
.00646 
.00753 
.00860 
.00966 
.01072 
.01178 

.01283 

.01389 
.01494 
.01598 
.01703 


438i3 
60618 
5o548 
i3738 
5o3i9 
60422 
44179 
01718 
33167 
38654 
i83o5 
72247 
oo6o3 
03498 
8io54 
33393 


1 .o425 

1 .o45o 

1 .0475 

i .o5oo 

o525 

o55o 

0575 

0600 

0625 

o65o 

1 .0675 

1 .0700 

1 .0725 

1 .0750 

1 .0775 

1 .0800 


.01807 
.01911 

.020l5 

.02118 

.02232 

. 02325 

.02428 
,o253o 
.02632 
.02734 
,02836 
.02938 
,o3o39 
.o3i4o 
.o324i 
.o3342 


6o636 
62904 
4o3i6 
92991 

2io45 
24596 
03760 
58653 

89387 
96078 
7S837 
37777 
73009 
84643 
72788 
37j55 


NUMBERS  OFTEN  USED  IN  CALCULATIONS. 


Circumference  of  a  circle  to  diameter  1  ) 

Surface  of  a  sphere  to  diameter  1 > =  3.1415926 

Area  of  a  circle  to  radius  1 ) 

Area  of  a  circle  to  diameter  1 =r  .  7853982 

Capacity  of  a  sphere  to  diameter  1 =  .5235988 

Capacity  of  a  sphere  to  radius  1 —  4-1887902 

I~3.i4i5926 =  o.3 1 83099 

Arc  equal  to  radius  expressed  in  degrees =  57°.  2957795 

Arc  equal  to  radius  expressed  in  seconds =  206264"  •  8 

Length  of  1  degree  in  parts  of  radius =  .01 74533 

Length  of  1  minute  in  parts  of  radius =  .  0002909 

Sine  of  1  second =  .ooooo485 

Sine  of  2  seconds =  .00000970 

Sine  of  3  seconds =  .ooooi454 

Sine  of  4  seconds » =  .00001939 

Sine  of  5  seconds —  .00002424 

Sine  of  6  seconds —  ■  .00002909 

Sine  of  7  seconds ~  .00003394 

Sine  of  8  seconds =  .00003879 

Sine  of  9  seconds =  .oooo4363 

Base  of  Napier's  system  of  logarithms =  2  .7182818 

Modulus  of  the  common  logarithms : .  =  .4342945 

36o  degrees  expressed  in  seconds s=  1296000 

24  hours  expressed  in  seconds —  864oo 

Number  of  feet  in  one  mile r=  5280 


Logarithms. 
0.497l5o 

9.895090 
9.718999 
O.622089 

9.5o285o 
1 .758123 
5.3i4425 
8.241877 
6.463726 
4.6B5575 
4.986605 
5. 162696 
5.287635 
5.384545 
5.463726 
5.53o673 
5.588665 
5.639817 
0.434294 
9.637784 
6.112605 
4»9365i4 
3.722634 


THE  END. 


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TREATISE  OX  METEOROLOGY.    308  pp.,  $1  75. 


55 


THE  LIBRARY 
UNIVERSITY  OF  CALIFORNIA 

Santa  Barbara 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW. 


Series  9482 


IIMIIIIIIIIIIIIIIHIII 


Illl  mi     1 1    I  minimi 

3  1205  01077  5821 


II I II I  III  III  lllll Illl  I 

AA      000121462    6 


